Updated on 2025/04/22

写真a

 
ITO Hiromichi
 
Organization
Faculty of Science and Engineering Professor
Other responsible organization
Mathematics Course of Graduate School of Science and Engineering, Master's Program
Mathematics Course of Graduate School of Science and Engineering, Doctoral Program
Contact information
The inquiry by e-mail is 《here》
External link

Degree

  • 博士（理学） ( 慶應義塾大学 )

  • 修士（理学） ( 慶應義塾大学 )

Education

  • 2004.3
     

    Keio University   doctor course   completed

  • 2001.3
     

    Keio University   master course   completed

  • 1999.3
     

    Keio University   graduated

Research History

  • 2025.4 - Now

    Chuo University   Faculty of Science and Engineering Department of Mathematics   Professor

Professional Memberships

  • 2022.10 - Now

    Inverse Problems International Association

  • 2005.4 - Now

    The Japan Society for Industrial and Applied Mathematics

  • 2000.9 - Now

    The mathematical society of Japan

  • 2013.10 - 2025.3

    The Japan Society of Mathematical Education

Research Interests

  • Singular integral equations

  • Fracture Mechanics

  • theory of elasticity

  • Analysis of singularities of corner and crack

  • 特異型積分方程式

  • 破壊力学

  • 偏微分方程式論

  • 弾性理論

Research Areas

  • Natural Science / Mathematical analysis

  • Natural Science / Applied mathematics and statistics

Papers

  • Solution of viscoelastic creep models for anisotropic materials with linear relation between strain and stress but nonlinear with respect to time Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Gen Nakamura

    Applications in Engineering Science   22   100219 - 100219   2025.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

    DOI： 10.1016/j.apples.2025.100219

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  • Forward and inverse problems for creep models in viscoelasticity Reviewed International coauthorship International journal

    H. Itou, V. A. Kovtunenko, G. Nakamura

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences   382 ( 2277 )   20230295   2024.8

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1098/rsta.2023.0295

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  • Non-smooth variational problems and applications in mechanics Reviewed International coauthorship International journal

    Victor A. Kovtunenko, Hiromichi Itou, Alexander M. Khludnev, Evgeny M. Rudoy

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences   382 ( 2277 )   20230310   2024.8

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1098/rsta.2023.0310

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  • Well-posedness of the governing equations for a quasi-linear viscoelastic model with pressure-dependent moduli in which both stress and strain appear linearly Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    Zeitschrift für angewandte Mathematik und Physik   75 ( 1 )   22   2024.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    <jats:title>Abstract</jats:title><jats:p>The response of a body described by a quasi-linear viscoelastic constitutive relation, whose material moduli depend on the mechanical pressure (that is one-third the trace of stress) is studied. The constitutive relation stems from a class of implicit relations between the histories of the stress and the relative deformation gradient. A-priori thresholding is enforced through the pressure that ensures that the displacement gradient remains small. The resulting mixed variational problem consists of an evolutionary equation with the Volterra convolution operator; this equation is studied for well-posedness within the theory of maximal monotone graphs. For isotropic extension or compression, a semi-analytic solution of the quasi-linear viscoelastic problem is constructed under stress control. The equations are studied numerically with respect to monotone loading both with and without thresholding. In the example, the thresholding procedure ensures that the solution does not blow-up in finite time.
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    DOI： 10.1007/s00033-023-02160-0

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  • A generalization of the Kelvin–Voigt model with pressure‐dependent moduli in which both stress and strain appear linearly Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    Mathematical Methods in the Applied Sciences   46 ( 14 )   15641 - 15654   2023.9

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1002/mma.9417

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  • Poroelastic problem of a non-penetrating crack with cohesive contact for fluid-driven fracture Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Nyurgun P. Lazarev

    Applications in Engineering Science   15   100136 - 100136   2023.5

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

    DOI： 10.1016/j.apples.2023.100136

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  • Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body Reviewed International journal

    Takahito Kashiwabara, Hiromichi Itou

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences   380 ( 2236 )   20220225   2022.11

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1098/rsta.2022.0225

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  • Non-smooth variational problems and applications Reviewed International coauthorship International journal

    Victor A. Kovtunenko, Hiromichi Itou, Alexander M. Khludnev, Evgeny M. Rudoy

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences   380 ( 2236 )   20210364   2022.11

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1098/rsta.2021.0364

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  • Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    Mathematical Models and Methods in Applied Sciences   32 ( 07 )   1475 - 1492   2022.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：World Scientific Pub Co Pte Ltd  

    <jats:p> A novel class of implicit constitutive relations is studied, wherein the stress and the linearized strain appear linearly, that describe material response in elastic porous bodies like rocks, ceramics, concrete, cement, bones and metals. The constitutive relation is applied to a body with a crack subjected to non-penetration conditions between the opposite crack faces. To treat well-posedness of a corresponding variational inequality, we rely on a new approximation by thresholding dilatation and apply the Lions existence theorem on pseudo-monotone variational inequalities. An analytical solution to a specific example (without crack) under uniform triaxial loading is constructed, wherein blow-up can take place at a finite load, and this difficulty is overcome within a thresholding approximation so that blow-up does not occur. </jats:p>

    DOI： 10.1142/s0218202522500336

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  • Asymptotic series solution for plane poroelastic model with non-penetrating crack driven by hydraulic fracture Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Nyurgun P. Lazarev

    Applications in Engineering Science   10   100089 - 100089   2022.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

    DOI： 10.1016/j.apples.2022.100089

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  • Unique solvability of crack problem with time-dependent friction condition in linearized elastodynamic body Reviewed International journal

    Itou, H., Kashiwabara, T.

    Журнал «Математические заметки СВФУ»   28 ( 3 )   121 - 134   2021.10

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Северо-Восточный федеральный университет имени М.К. Аммосова  

    Журнал «Математические заметки СВФУ», Выпуск 3 (111) 2021

    DOI： 10.25587/SVFU.2021.38.33.008

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  • Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Evgeny M. Rudoy

    Applications in Engineering Science   7   100060 - 100060   2021.9

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

    DOI： 10.1016/j.apples.2021.100060

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  • On an Implicit Model Linear in Both Stress and Strain to Describe the Response of Porous Solids Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    Journal of Elasticity   144 ( 1 )   107 - 118   2021.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media {LLC}  

    DOI： 10.1007/s10659-021-09831-x

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  • Asymptotic Justification of the Models of Thin Inclusions in anElastic Body in the Antiplane Shear Problem Reviewed International coauthorship International journal

    E. M. Rudoy, H. Itou, N. P. Lazarev

    Journal of Applied and Industrial Mathematics   15 ( 1 )   129 - 140   2021.4

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Pleiades Publishing Ltd  

    DOI： 10.1134/s1990478921010117

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  • Lagrange multiplier approach to unilateral indentation problems: Well-posedness and application to linearized viscoelasticity with non-invertible constitutive response Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   31 ( 3 )   649 - 674   2021.3

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    Language：English  

    DOI： 10.1142/S0218202521500159

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  • Equilibrium problems for Kirchhoff–Love plates with nonpenetration conditions for known configurations of crack edges Reviewed International coauthorship International journal

    Lazarev, N.P., Itou, H.

    Журнал «Математические заметки СВФУ»   27 ( 3 )   52 - 65   2020.10

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：Северо-Восточный федеральный университет имени М.К. Аммосова  

    The paper focuses on nonlinear problems describing the equilibrium of Kirchhoff–Love plates with cracks. We assume that under an appropriate load, plates have special deformations with previously known configurations of edges near a crack. Owing to this particular case, we propose two types of new nonpenetration conditions that allow us to more precisely describe the possibility of contact interaction of crack faces. These conditions correspond to two special cases of configurations of plate edges. In each case, the nonpenetration conditions are given in the form of a system of equalities and inequalities. For initial variational statements, we prove the existence and uniqueness of solutions in an appropriate Sobolev space. Assuming that the solutions are sufficiently smooth, we have found differential statements that are equivalent to the corresponding variational formulations. The relations of the obtained differential statements are compared with the well-known setting of an equilibrium problem for a Kirchhoff–Love plate with the general nonpenetration condition on crack faces.

    DOI： 10.25587/SVFU.2020.75.68.005

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  • Parameter interdependence of dynamic self-similar crack with distance-weakening friction Reviewed International journal

    Shiro Hirano, Hiromichi Itou

    Geophysical Journal International   2020.8

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    <jats:title>Summary</jats:title>
    <jats:p>In several analytical and numerical studies, the slip rate function and energy release rate for dynamic self-similar crack growth have been investigated, and the results obtained have contributed to a theoretical understanding and estimation of on-fault energetics. However, the relationships among physical parameters, including stress state, process zone size, rupture velocity, peak slip rate, and energy release rate, are still unclear. Therefore, the aim of this study is to derive an analytical solution of the slip rate distribution of antiplane self-similar crack growth under distance-weakening friction that mimics slip-weakening friction. To satisfy the condition that the slip rate starts from zero at the rupture front, a trade-off relationship among rupture velocity, process zone size, and breakdown stress-to-stress drop ratio is proposed. The peak slip rate, slip-weakening distance, and fracture energy obtained using the proposed model provide a possible mechanism for the determination of the rupture velocity and the estimation of the fracture energy of the self-similar crack growth, based on the seismic observables.</jats:p>

    DOI： 10.1093/gji/ggaa392

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  • The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    International Journal of Engineering Science   151   103272 - 103272   2020.6

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    Publishing type：Research paper (scientific journal)   Publisher：Elsevier {BV}  

    DOI： 10.1016/j.ijengsci.2020.103272

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  • Modeling of bonded elastic structures by a variational method: Theoretical analysis and numerical simulation Reviewed International coauthorship International journal

    Alexey Furtsev, Hiromichi Itou, Evgeny Rudoy

    International Journal of Solids and Structures   182-183   100 - 111   2020.1

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.ijsolstr.2019.08.006

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  • Identification of an unknown shear force in a cantilever Euler–Bernoulli beam from measured boundary bending moment Reviewed International coauthorship International journal

    Hiromichi Itou

    Journal of Inverse and Ill-posed Problems   27 ( 6 )   859 - 876   2019.8

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1515/jiip-2019-0020

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  • Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous Kirchhoff–Love plates with a crack Reviewed International coauthorship International journal

    Lazarev, N., Itou, H.

    Mathematics and Mechanics of Solids   24 ( 12 )   3743 - 3752   2019.6

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1177/1081286519850608

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  • Well-posedness of the problem of non-penetrating cracks in elastic bodies whose material moduli depend on the mean normal stress Reviewed International coauthorship International journal

    Itou, H., Kovtunenko, V.A., Rajagopal, K.R.

    International Journal of Engineering Science   136   17 - 25   2019.3

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.ijengsci.2018.12.005

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  • Revealing cracks inside conductive bodies by electric surface measurements Reviewed International coauthorship International journal

    Hauptmann, A., Ikehata, M., Itou, H., Siltanen, S.

    Inverse Problems   35 ( 2 )   025004 (24pp)   2019.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1088/1361-6420/aaf273

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  • Crack problem within the context of implicitly constituted quasi-linear viscoelasticity Reviewed International coauthorship International journal

    Itou, H., Kovtunenko, V.A., Rajagopal, K.R.

    Mathematical Models and Methods in Applied Sciences   29 ( 2 )   355 - 372   2019.2

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    Language：English   Publishing type：Research paper (scientific journal)  

    <jats:p> A quasi-linear viscoelastic relation that stems from an implicit viscoelastic constitutive body containing a crack is considered. The abstract form of the response function is given first in [Formula: see text], [Formula: see text], due to power-law hardening; second in [Formula: see text] due to limiting small strain. In both the cases, sufficient conditions on admissible response functions are formulated, and corresponding existence theorems are proved rigorously based on the variational theory and using monotonicity methods. Due to the presence of a Volterra convolution operator, an auxiliary-independent variable of velocity type is employed. In the case of limiting small strain, the generalized solution of the problem is provided within the context of bounded measures and expressed by a variational inequality. </jats:p>

    DOI： 10.1142/S0218202519500118

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  • A priori estimates for the general dynamic Euler–Bernoulli beam equation: Supported and cantilever beams Reviewed International coauthorship International journal

    Hasanov, A., Itou, H.

    Applied Mathematics Letters   87   141 - 146   2019.1

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.aml.2018.07.038

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  • О РЕГУЛЯРНОСТИ РЕШЕНИЯ В ЗАДАЧЕ О РАВНОВЕСИИ ПЛАСТИНЫ ТИМОШЕНКО, СОДЕРЖАЩЕЙ НАКЛОННУЮ ТРЕЩИНУ Reviewed International coauthorship International journal

    Hiromichi Itou

    №1 (2018)   25 ( 1 )   38 - 49   2018.5

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    Language：Russian   Publishing type：Research paper (scientific journal)  

    Исследуется задача о равновесии упругой трансверсально-изотропной пластины (модели Тимошенко), содержащей сквозную наклонную трещину. Считается что трещина не выходит на внешнюю границу. В исходном состоянии предполагается, что противоположные берега соприкасаются друг с другом. При этом трещина описывается с помощью поверхности, которая удовлетворят определенным предположениям. На кривой, задающей трещину в срединной плоскости, ставится краевое условие в виде неравенства, описывающее непроникание противоположных берегов трещины. На внешней границе заданы однородные условия Дирихле. Установлена локальная дополнительная гладкость решения по сравнению с заданной в вариационной формулировке при определенных условиях на поверхность, задающую трещину. Доказана бесконечная дифференцируемость функции решения при дополнительных предположениях на функцию, задающую внешние нагрузки, а также на значения функций перемещений вблизи кривой, описывающей трещину.

    DOI： 10.25587/svfu.2018.1.12767

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  • On the states of stress and strain adjacent to a crack in a strain-limiting viscoelastic body Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A Kovtunenko, Kumbakonam R Rajagopal

    Mathematics and Mechanics of Solids   23 ( 3 )   433 - 444   2018.3

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SAGE Publications Inc.  

    The viscoelastic Kelvin–Voigt model is considered within the context of quasi-static deformations and generalized with respect to a nonlinear constitutive response within the framework of limiting small strain. We consider a solid possessing a crack subject to stress-free faces. The corresponding class of problems for strain-limiting nonlinear viscoelastic bodies with cracks is considered within a generalized formulation stated as variational equations and inequalities. Its generalized solution, relying on the space of bounded measures, is proved rigorously with the help of an elliptic regularization and a fixed-point argument.

    DOI： 10.1177/1081286517709517

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  • Contacting crack faces within the context of bodies exhibiting limiting strains Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam, R. Rajagopal

    JSIAM Letters   9   61 - 64   2017.9

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    Authorship：Lead author   Language：English   Publisher：The Japan Society for Industrial and Applied Mathematics  

    <p> A nonlinear crack problem subject to a non-penetration inequality is considered within the framework of the limiting small strain approach, which does not suffer from the inconsistency of infinite strain at the crack tip. Based on the concept of a generalized solution, sufficient conditions proving the well-posedness of the problem are established and analyzed.</p>

    DOI： 10.14495/jsiaml.9.61

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  • Nonlinear elasticity with limiting small strain for cracks subject to non-penetration Reviewed International coauthorship International journal

    Hiromichi Itou, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    MATHEMATICS AND MECHANICS OF SOLIDS   22 ( 6 )   1334 - 1346   2017.6

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SAGE PUBLICATIONS LTD  

    A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a non-smooth viscosity solution which is described by generalized variational inequalities and coincides with the weak solution in the smooth case. The well-posedness is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.

    DOI： 10.1177/1081286516632380

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  • 卓越した生徒のための数学教育プログラムの開発1 ─パート2：コンピュータ実験教材と、ゼミ形式を中心とする、 GSCにおける卓越した意欲能力を有する高校生向けの教育─ Reviewed

    佐古彰史, 清水克彦, 伊藤弘道

    東京理科大学教職教育研究   ( 1 )   93 - 100   2017.3

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    Language：Japanese  

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  • 卓越した生徒のための数学教育プログラムの開発1 ─パート1：現物実験をとりいれたGSCにおける卓越した意欲能力を有する高校生向け教材の開発と実践を踏まえて─ Reviewed

    佐古彰史, 伊藤弘道, 清水克彦

    東京理科大学教職教育研究   ( 1 )   85 - 91   2017.3

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  • Mathematical Analysis of Continuum Mechanics and Industrial Applications

    Hiromichi Itou

    2017

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    Publisher：Mathematics for Industry  

    DOI： 10.1007/978-981-10-2633-1

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  • On Singularities in 2D Linearized Elasticity Reviewed International journal

    Hiromichi Itou

    MATHEMATICAL ANALYSIS OF CONTINUUM MECHANICS AND INDUSTRIAL APPLICATIONS   26   35 - 47   2017

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    Authorship：Lead author   Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER-VERLAG SINGAPORE PTE LTD  

    The aim of this paper is to introduce some convergent expansion formulae of solutions of two-dimensional linearized elasticity equation so-called as Navier's equation around a crack tip and a tip of thin rigid inclusion, explicitly. In particular, three boundary value problems are treated; the first case is that a homogeneous and anisotropic body has a linear crack; the second case is that two different isotropic homogeneous bodies have an interfacial crack under the non-penetration condition and the frictional condition in Coulomb's law; the third case is that a homogeneous and isotropic body has a rigid line inclusion. Moreover, the paper intends to clarify how the order of singularities in expansions is determined, which depends on the geometry of the material, the governing equation, boundary conditions, material properties, and so on.

    DOI： 10.1007/978-981-10-2633-1_4

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  • On delaminated thin Timoshenko inclusions inside elastic bodies Reviewed International coauthorship International journal

    H. Itou, A. M. Khludnev

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES   39 ( 17 )   4980 - 4993   2016.11

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：WILEY  

    In the paper, we consider equilibrium problems for 2D elastic bodies with thin inclusions modeled in the frame of Timoshenko beam theory. It is assumed that a delamination of the inclusion takes place thus providing a presence of cracks between the inclusion and the elastic body. Nonlinear boundary conditions at the crack faces are imposed to prevent a mutual penetration between the faces. Different problem formulations are analyzed: variational and differential. Dependence on physical parameters characterizing the mechanical properties of the inclusion is investigated. The paper provides a rigorous asymptotic analysis of the model with respect to such parameters. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain rigid inclusions and cracks with the non-penetration conditions, respectively. Also anisotropic inclusions with parameters are analyzed when parameters tend to zero and infinity. In particular, in the limit, we obtain the so called semi-rigid inclusions. Copyright (C) 2014 JohnWiley & Sons, Ltd.

    DOI： 10.1002/mma.3279

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  • The enclosure method for an inverse problem arising from a spot welding Reviewed International journal

    Masaru Ikehata, Hiromichi Itou, Akira Sasamoto

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES   39 ( 13 )   3565 - 3575   2016.9

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：WILEY-BLACKWELL  

    A two dimensional version of a reconstruction problem of an unknown weld on the interface between two electric conductive plates is considered. It is assumed that the two plates have a same known isotropic homogeneous conductivity, and the line where the welding area is located is known. Under these assumptions, an explicit extraction formula of the location of the tips of the welding area on the line from a single set of an electric current density and the corresponding voltage potential on the boundary of the material formed by the plates is given. This result may have possibility of application to quality evaluation of spot welding fixation strength of a lamina. Copyright (C) 2015 John Wiley & Sons, Ltd.

    DOI： 10.1002/mma.3799

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  • Fictitious domain method for an equilibrium problem of the Timoshenko-type plate with a crack crossing the external boundary at zero angle Reviewed International coauthorship International journal

    N. P. Lazarev, H. Itou, N. V. Neustroeva

    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS   33 ( 1 )   63 - 80   2016.2

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    Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER JAPAN KK  

    The equilibrium problems for homogeneous and inhomogeneous plates with a crack is considered. We impose the nonpenetration condition, which has the form of inequality (such as Signorini type condition), on the crack faces. In this paper, we deal with the cases that the crack intersects the external boundary at zero angle (on the mid-plane). Using the fictitious domain method, we establish the unique solvability of four equilibrium problems for different cases of non-Lipschitz domains. In these cases a precise connection between equilibrium problems for a plate contacting with a rigid obstacle and for a plate with a crack is identified.

    DOI： 10.1007/s13160-015-0200-x

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  • Timoshenko Thin Inclusions in an Elastic Body with Possible Delamination Reviewed International coauthorship International journal

    H. Itou, G. Leugering, A. M. Khludnev

    DOKLADY PHYSICS   59 ( 9 )   401 - 404   2014.9

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：MAIK NAUKA/INTERPERIODICA/SPRINGER  

    DOI： 10.1134/S1028335814090018

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  • Тонкие включения Тимошенко в упругом теле с возможным отслоением

    Х. Итоу, Г. Лойгеринг, А. М. Хлуднев

    Доклады Академии наук   2014

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.7868/s0869565214250082

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  • On reconstruction of a cavity in a linearized viscoelastic body from infinitely many transient boundary data Reviewed International journal

    Masaru Ikehata, Hiromichi Itou

    INVERSE PROBLEMS   28 ( 12 )   125003 (19pp)   2012.12

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    In this paper, a reconstruction problem of a cavity in a linearized viscoelastic body from dynamical boundary data is considered. As a result, we establish a formula extracting three kinds of information about the unknown cavity: the support function, the distance from an outer point of the body and the minimum radius of the open ball including the cavity centered at a point, with infinitely many sets of the boundary data. In the formula, observation time can be taken to be arbitrary.

    DOI： 10.1088/0266-5611/28/12/125003

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  • Asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity Reviewed International coauthorship International journal

    Hiromichi Itou, A. M. Khludnev, E. M. Rudoy, A. Tani

    ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK   92 ( 9 )   716 - 730   2012.9

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    We consider an asymptotic behaviour of a solution near a tip of a rigid line inclusion in two dimensional homogeneous isotropic linearized elasticity. By means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution around there. Furthermore, we give expressions of the invariant integral and the Irwin's formula.

    DOI： 10.1002/zamm.201100157

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  • NUMERICAL SOLUTIONS OF LINEAR SINGULAR INTEGRAL EQUATIONS BY MEANS OF TIKHONOV REGULARIZATION AND REPRODUCING KERNELS Reviewed International coauthorship International journal

    L. P. Castro, H. Itou, S. Saitoh

    HOUSTON JOURNAL OF MATHEMATICS   38 ( 4 )   1261 - 1276   2012

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    In this paper, a reproducing kernel method is proposed to perform the analysis of different types of singular integral equations. We will be mostly interested in linear singular integral equations of Cauchy type which have functions as coefficients (for which an equation of Carleman type serves as a model). Anyway, due to the nature of our method we will be also able to study corresponding so-called discrete singular integral equations and inverse source problems. All these include a new concept and method which provides practical and numerical solutions of very general linear singular integral equations by combining the two theories of Tikhonov regularization and reproducing kernels.

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  • The interface crack with coulomb friction between two bonded dissimilar elastic media Reviewed International coauthorship International journal

    Itou, H., Kovtunenko, V.A., Tani, A.

    Applications of Mathematics   56 ( 1 )   69 - 97   2011.1

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    DOI： 10.1007/s10492-011-0010-7

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  • On Convergent Expansions of Solutions of the Linearized Elasticity Equation near Singular Points Reviewed International journal

    Hiromichi Itou

    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C   1389   465 - 468   2011

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    In this paper, we introduce some convergent expansion formulae of solutions of two dimensional linearized elasticity equation (called Navier's equation) around singular points such as a corner and a crack tip.

    DOI： 10.1063/1.3636764

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  • On reconstruction of an unknown polygonal cavity in a linearized elasticity with one measurement Reviewed International journal

    M. Ikehata, H. Itou

    INTERNATIONAL CONFERENCE ON INVERSE PROBLEMS 2010   290 ( 1 )   012005   2011

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    In this paper we consider a reconstruction problem of an unknown polygonal cavity in a linearized elastic body [16]. For this problem, an extraction formula of the convex hull of the unknown polygonal cavity is established by means of the enclosure method introduced by Ikehata [2, 4]. The advantages of our method are that it needs only a single set of boundary data and we do not require any a priori assumptions for the unknown polygonal cavity and any constraints on boundary data. The theoretical formula may have possibility of application in nondestructive evaluation.

    DOI： 10.1088/1742-6596/290/1/012005

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  • Extracting the support function of a cavity in an isotropic elastic body from a single set of boundary data Reviewed International journal

    Ikehata, M., Itou, H.

    Inverse Problems   25 ( 10 )   105005 (21pp)   2009.10

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    DOI： 10.1088/0266-5611/25/10/105005

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  • Applications of reproducing kernels to linear singular integral equations through the Tikhonov regularization Reviewed International journal

    H. Itou, S. Saitoh

    More Progresses in Analysis: Proceedings of the 5th International ISAAC Congress   135 - 142   2009.5

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  • An inverse problem for a linear crack in an anisotropic elastic body and the enclosure method Reviewed International journal

    Masaru Ikehata, Hiromichi Itou

    INVERSE PROBLEMS   24 ( 2 )   025005 (21pp)   2008.4

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    This paper considers the problem: extract information about the location and shape of an unknown crack from a single set of the surface displacement field and traction on the boundary of an arbitrary homogeneous and anisotropic elastic plate. In states of both plane stress and plane strain, an extraction formula of an unknown crack is given provided: the crack is linear; one of two end points of the crack is known and located on the boundary of the body; a well-controlled surface traction is given on the boundary of the body.

    DOI： 10.1088/0266-5611/24/2/025005

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  • Enclosure method and reconstruction of a linear crack in an elastic body Reviewed International journal

    M. Ikehata, H. Itou

    Journal of Physics: Conference Series   135 ( 1 )   012052   2008

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    In this paper we report a recent application of the idea of the enclosure method to an inverse problem related to a crack (inverse crack problem) in an elastic body. The problem is to extract information about the location and shape of an unknown crack from a single set of the surface displacement field and traction on the boundary of an arbitrary homogeneous elastic plate. Both anisotropic and isotropic bodies are considered. In states of both plane stress and plane strain, an extraction formula of an unknown crack is given provided: the crack is linear
    one of two end points of the crack is known and located on the boundary of the body
    a well-controlled surface traction is given on the boundary of the body. © 2008 IOP Publishing Ltd.

    DOI： 10.1088/1742-6596/135/1/012052

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  • Analytical and Numerical Solutions of Linear Singular Integral Equations Reviewed International journal

    Hiromichi Itou, Saburou Saitoh

    International Journal of Applied Mathematics and Statistics   12 ( D07 )   76 - 89   2007.12

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  • Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data Reviewed International journal

    Masaru Ikehata, Hiromichi Itou

    INVERSE PROBLEMS   23 ( 2 )   589 - 607   2007.4

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    An inverse problem related to a crack in elastostatics is considered. The problem is: extract information about the location and shape of an unknown crack from a single set of the surface displacement field and traction on the boundary of the elastic body. This is a typical problem from the non-destructive testing of materials. A version in a plane problem of elastostatics is considered. It is shown that, in a state of plane strain, the enclosure method which was introduced by Ikehata yields the extraction formula of an unknown crack provided: the crack is linear; one of the two end points of the crack is known and located on the boundary of the body; a well-controlled surface traction is given on the boundary of the body.

    DOI： 10.1088/0266-5611/23/2/008

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  • Shape derivative of energy functional in an infinite elastic strip with a semi-infinite crack Reviewed International journal

    Hiromichi Itou, Atusi Tani

    Tokyo Journal of Mathematics   29 ( 2 )   385 - 397   2006

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    In this paper we study linear elasticity equations in an infinite elastic strip with a semi-infinite crack. We find the derivative of the energy functional as the crack shifts with an angle. Then we obtain the formula given by surface force and the angle. © 2006 International Academic Printing Co. Ltd. All rights reserved.

    DOI： 10.3836/tjm/1170348173

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  • Existence of a weak solution in an infinite viscoelastic strip with a semi-infinite crack Reviewed International journal

    Hiromichi Itou

    Hyperbolic Problems: Theory, Numerics, Applications   II   41 - 48   2006

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  • Existence of a weak solution in an infinite viscoelastic strip with a semi-infinite crack Reviewed International journal

    H Itou, A Tani

    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES   14 ( 7 )   975 - 986   2004.7

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    Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

    We study an initial-boundary value problem in an infinite viscoelastic strip with a semi-infinite fixed crack. For this problem we prove the existence and uniqueness of a weak solution which is prescribed on each side of the extended crack in Sobolev-type spaces.

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  • A boundary value problem for an infinite elastic strip with a semi-infinite crack Reviewed International journal

    H Itou, A Tani

    JOURNAL OF ELASTICITY   66 ( 3 )   193 - 206   2002

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    In this paper we study a boundary value problem for an infinite elastic strip with a semi-infinite crack. By using the single and double layer potentials this problem is reduced to a singular integral equation, which is uniquely solved in the Holder spaces by the Fredholm alternative.

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Books

  • Non-smooth variational problems and applications in mechanics International journal

    Victor A. Kovtunenko, Hiromichi Itou, Alexander M. Khludnev, Evgeny M. Rudoy（ Role： Joint editor）

    The Royal Society Publishing  2024.8  （ ISBN:9781782527183 ）

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  • Non-smooth variational problems and applications International journal

    Victor A. Kovtunenko, Hiromichi Itou, Alexander M. Khludnev, Evgeny M. Rudoy（ Role： Joint editor）

    The Royal Society Publishing  2022.11  （ ISBN:9781782526032 ）

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  • Mathematical Analysis of Continuum Mechanics and Industrial Applications III -Proceedings of the International Conference CoMFoS18- (Mathematics for Industry Volume 34)

    Itou, H., Hirano, S., Kimura, M., Kovtunenko, V.A., Khludnev, A.M.（ Role： Edit）

    Springer Singapore  2020.8  （ ISBN:9789811560613 ）

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  • 理工系の基礎「数学 Ⅰ」

    小谷佳子, 伊藤弘道, 加藤圭一, 矢部博, 江川嘉美, 太田雅人, 横田智巳, 眞田克典, 関川浩（ Role： Joint author）

    丸善出版  2018.1  （ ISBN:9784621302491 ）

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  • Mathematical Analysis of Continuum Mechanics and Industrial Applications

    Hiromichi Itou, Masato Kimura, Vladimir Chalupecky, Kohji Ohtsuka, Daisuke Tagami, Akira Takada（ Role： Edit）

    Springer Singapore  2016.11  （ ISBN:9789811026324 ）

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  • 応用数理ハンドブック

    日本応用数理学会, 監修, 薩摩順吉, 大石進一, 杉原正顕, 名のうち, 番目, 五十音順（ Role： Joint author）

    朝倉書店  2013.11  （ ISBN:9784254111415 ）

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MISC

  • 平均垂直応力に依存する係数をもつ弾性体の数学解析

    伊藤弘道

    日本大学経済学部 研究紀要 一般教育・外国語・保健体育   ( 98 )   223 - 233   2023.9

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  • On unilateral contact problems with friction for an elastic body with cracks

    Alexey I. Furtsev, Hiromichi Itou, Victor A. Kovtunenko, Evgeny M. Rudoy, Atusi Tani

    RIMS Kôkyûroku   2174   2021.2

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  • On an inverse crack problem in a linearized elasticity by the enclosure method

    Hiromichi Itou

    Hokkaido University Technical Report Series in Mathematics   179   89 - 98   2020.7

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    DOI： 10.14943/94913

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  • On reconstruction of polygonal cavities in an elastic body with one measurement

    Masaru Ikehata, Hiromichi Itou

    Hokkaido University Technical Report Series in Mathematics   141   44 - 52   2009

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  • On reconstruction of an unknown polygonal cavity in an isotropic elastic body with one measurement

    Masaru Ikehata, Hiromichi Itou

    Seminar Notes of Mathematical Sciences   12   25 - 40   2009

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  • On an inverse problem for a linear crack in an anisotropic elastic body

    Masaru Ikehata, Hiromichi Itou

    Seminar Notes of Mathematical Sciences   11   64 - 80   2008

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  • Construction of approximate solutions for singular integral equations by using the theory of reproducing kernels

    Hiromichi Itou, Saburou Saitoh

    RIMS Kokyuroku   1618   160 - 174   2008

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    CiNii Books

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    Other Link： http://hdl.handle.net/2433/140184

  • Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data

    Masaru Ikehata, Hiromichi Itou

    Seminar Notes of Mathematical Sciences   10   50 - 66   2007

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  • On inverse crack problems in elastostatics

    Masaru Ikehata, Hiromichi Itou

    PAMM   7 ( 1 )   1090805 - 1090806   2007

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    Language：English   Publisher：Wiley  

    DOI： 10.1002/pamm.200700642

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  • A boundary-value problem for an infinite elastic strip with a semi-infinite crack

    Hiromichi Itou, Atusi Tani

    PAMM   7 ( 1 )   1042601 - 1042602   2007

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    Language：English   Publisher：Wiley  

    DOI： 10.1002/pamm.200700265

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  • On a problem for a kinked crack

    Hiromichi Itou

    破壊現象の数理, Seminar on Mathematical Sciences, Keio University   ( 34 )   157 - 171   2005

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  • On a problem for a kinked crack

    Hiromichi Itou

    Seminar Notes of Mathematical Sciences   8   25 - 34   2005

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  • A boundary value problem and crack propagation in an infinite (visco)elastic strip with a semi-infinite crack

    Hiromichi Itou

    Seminar Notes of Mathematical Sciences   7   39 - 49   2004

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  • A boundary value problem and crack propagation in an infinite (visco)elastic strip with a semi-infinite crack

    Hiromichi Itou, Atusi Tani

    RIMS Kokyuroku   1353   49 - 71   2004

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    Other Link： http://hdl.handle.net/2433/25146

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Presentations

  • 破壊現象の数学解析と逆問題 Invited

    伊藤弘道

    第48回調和解析定例セミナー  2025.4 

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    Language：Japanese   Presentation type：Oral presentation (general)  

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  • 微小ひずみ下での様々な粘弾性体モデルとその数学解析

    伊藤 弘道

    日本応用数理学会 第21回研究部会連合発表会  2025.3 

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  • Mathematical modelling on linearized viscoelasticity with fractional derivatives

    Hiromichi Itou

    Russia-Japan-India Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications"  2024.12 

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  • On frictional crack problems in linearized elasticity International conference

    Hiromichi Itou

    Finland-Japan Workshop in Industrial and Applied Mathematics  ( University of Helsinki )   2024.8 

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  • On inverse and forward problems of some viscoelastic models International conference

    Hiromichi Itou

    11th International Conference "Inverse Problems: Modeling and Simulation" (IPMS 2024), M16. Inverse Problem Theory for Innovation of Detection Methods  ( Paradise Bay Resort Hotel（マルタ） )   2024.5 

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  • 囲い込み法を用いたき裂の再構成の逆問題について

    伊藤弘道

    東京都立大学・数理解析セミナー  ( 東京都立大学南大沢キャンパス )   2023.12 

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  • き裂の再構成の逆問題

    伊藤弘道

    談話会  ( 広島大学理学部数学科 )   2023.12 

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  • On a generalization Kelvin–Voigt model with pressure-dependent moduli International conference

    Hiromichi Itou, Victor Kovtunenko, Kumbakonam Rajagopal

    10th International Congress on Industrial and Applied Mathematics (ICIAM2023), MS[00085]: Singular Problems in Mechanics,  ( 早稲田大学（東京） )   2023.8 

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  • 囲い込み法を用いた線形弾性体におけるき裂の再構成について

    池畠優、伊藤弘道

    日本応用数理学会2022年度年会  ( 北海道大学（ハイブリッド開催） )   2022.9 

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  • On inverse crack problems in linearized elastic bodies by the Enclosure method International conference

    Hiromichi Itou

    Theoretical and numerical trends in inverse problems and control for PDE's, and Hamilton-Jacobi equation: French-Italian-Japanese conference  ( CIRM(​Centre International de Rencontres Mathématiques) (Luminy, France) )   2022.6 

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  • 速度を含むSignorini型接触条件とTresca摩擦条件下での線形動弾性体方程式の一意可解性

    柏原 崇人,伊藤 弘道

    日本数学会2022年度年会 函数方程式論分科会  ( 埼玉大学（オンライン開催） )   2022.3 

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  • A remark on crack problems with time-dependent friction condition in linearized elastodynamic body International conference

    Hiromichi Itou, Takahito Kashiwabara

    The XXIII International Symposium on Mathematical Methods Applied to Science (XXIII SIMMAC)  ( オンライン開催（コスタリカ） )   2022.2 

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  • ある非線形(粘)弾性体モデルの数学解析

    伊藤弘道

    幾何学・連続体力学・情報科学の交差領域の探索(II)  ( 明治大学・中野キャンパス（オンライン開催） )   2021.12 

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  • On an inverse crack problem in a linearized elasticity by the enclosure method International conference

    Hiromichi Itou

    The 8th European congress of Mathematics, Nonsmooth Variational Methods for PDEs and Applications in Mechanics (MS - ID 8)  ( オンライン開催(スロベニア) )   2021.6 

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  • き裂問題の数学解析－摩擦・接触、非線形弾性体－

    伊藤弘道

    Elastic and dissipative motions of curves and interfaces in continuum media  ( オンライン開催 )   2021.6 

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  • 動的自己相似亀裂を表現する特異積分方程式の変数変換について

    平野史朗, 伊藤弘道

    日本応用数理学会 2021年 研究部会連合発表会  ( オンライン開催 )   2021.3 

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  • On unilateral indentation problems in viscoelasticity with non-invertible constitutive response

    伊藤 弘道

    Critical Exponent and Nonlinear Partial Differential Equations 2021  ( オンライン開催 )   2021.2 

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  • 粘弾性体におけるき裂問題と圧子押込み問題について

    伊藤弘道

    第３２回さいたま数理解析セミナー  ( オンライン開催 )   2020.12 

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  • On a flat-punch indentation problem within the context of linearized viscoelasticity International conference

    Hiromichi Itou

    The Second Russia-Japan Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications" - 20th Conference of Continuum Mechanics Focusing on Singularities (CoMFoS20)  ( オンライン開催 )   2020.12 

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  • Dynamic antiplane self-similar crack with distance-weakening friction: an analytical solution for source parameter estimation International conference

    Shiro Hirano, Hiromichi Itou

    American Geophysical Union Fall Meeting  ( online )   2020.12 

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  • 弾性体における摩擦を伴う接触問題について

    伊藤弘道

    第724回応用解析研究会  ( 早稲田大学 西早稲田キャンパス )   2020.11 

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  • 距離弱化型摩擦則を伴なう動的自己相似亀裂の解析解

    平野 史朗、伊藤 弘道

    日本地震学会2020年度秋季大会  ( オンライン会議 )   2020.10 

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  • On flat-punch indentation problems within the context of linearized viscoelasticity

    伊藤 弘道, Victor A. Kovtunenko, Kumbakonam R. Rajagopal

    日本数学会2020年度秋季総合分科会 函数方程式論分科会  ( 熊本大学（オンライン開催） )   2020.9 

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  • On an inverse crack problem in a linearized elasticity by the enclosure method

    伊藤弘道

    第45回偏微分方程式論札幌シンポジウム  ( 北海道大学(Webinar) )   2020.8 

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  • On some problems within the context of implicitly constituted (visco)elasticity with limiting small strain

    伊藤弘道

    松山解析セミナー2020  ( 愛媛大学 城北キャンパス )   2020.1 

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  • On unilateral contact problems with friction for an elastic body with cracks International conference

    Hiromichi Itou

    RIMS共同研究（公開型）「偏微分方程式による逆問題解析とその周辺」  ( 京都大学数理解析研究所 )   2020.1 

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  • On some problems for fracture phenomena International conference

    Hiromichi Itou

    Russia-Japan Workshop “Mathematical analysis of fracture phenomena for elastic structures and its applications”  ( Novosibirsk State University, Novosibirsk, Russia )   2019.11 

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  • き裂の再構成の逆問題について

    伊藤弘道

    情報数理談話会  ( 東北大学 大学院情報科学研究科 (青葉山キャンパス) )   2019.9 

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  • 逆問題の数学解析とEITへの応用

    伊藤 弘道

    「医療画像診断における逆問題」セミナー  ( 東京理科大学野田キャンパス )   2019.9 

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  • On Crack Problems for Nonlinear (Visco)Elasticity International conference

    Hiromichi Itou

    International Conference AIP2019: Applied Inverse Problems conference  ( Grenoble (フランス) )   2019.7 

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  • Detecting cracks in conductive bodies by the enclosure method International conference

    Hiromichi Itou

    International Conference AIP2019: Applied Inverse Problems conference  ( Grenoble (フランス) )   2019.7 

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  • On inverse crack problems in conductive bodies by the enclosure method International conference

    Hiromichi Itou

    The 11th Conference on Inverse Problems, Imaging and Applications  ( Lanzhou (China) )   2019.6 

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  • ある非線形(粘) 弾性体におけるき裂問題について

    伊藤弘道

    大分微分方程式研究集会  ( サテライトキャンパスおおいた（大分市） )   2018.9 

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  • On an interfacial self-similar crack problem in anti-plane deformation International conference

    Hiromichi Itou

    9th International Conference“Inverse Problems: Modeling and Simulation”  ( Paradise Bay Resort Hotel（マルタ） )   2018.5 

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  • On frictional problems in elasticity International conference

    Hiromichi Itou

    Seminar "Boundary-value problems in domains with nonsmooth boundaries"  ( Novosibirsk・Institute of hydrodynamics, Siberian branch of Russian Academy of Sciences (Russia) )   2018.3 

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  • 高速で拡大する自己相似な面外亀裂の特異積分方程式

    平野 史朗, 伊藤 弘道

    日本応用数理学会 第14回 研究部会連合発表会  ( 大阪大学工学部（吹田キャンパス） )   2018.3 

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  • ある非線形弾性体におけるき裂問題とその面外変形の場合について

    伊藤弘道

    第54回東工大数理解析セミナー  ( 東京工業大学 大岡山キャンパス )   2018.2 

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  • Contacting crack faces within the context of nonlinear elastic bodies exhibiting limiting strain International conference

    Hiromichi Itou

    2nd International Conference on "Modern Mathematical Methods and High Performance Computing in Science and Technology" (M3HPCST-2018)  ( Inderprastha Engineering College, Ghaziabad (インド) )   2018.1 

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  • On inverse problems of a crack and a cavity in linearized elasticity International conference

    Hiromichi Itou

    A3 Workshop on Applied Inverse Problems and Related Topics  ( 東京大学 )   2017.11 

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  • On inverse crack problems by means of the enclosure method International conference

    Hiromichi Itou

    The 15th Annual Meeting of the China Society for Industrial and Applied Mathematics(CSIAM2017), A3 Workshop on Modeling and Computation of Applied Inverse Problems  ( Qingdao, China )   2017.10 

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  • On direct and inverse problems involving cracks in elasticity International conference

    Hiromichi Itou

    Geometry and Inverse Problems  ( Tohoku University )   2017.10 

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  • き裂を含む領域における偏微分方程式の解析

    伊藤弘道

    2017 日本数学会 秋季総合分科会 函数方程式論分科会 特別講演  ( 山形大学 小白川キャンパス )   2017.9 

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  • 理科と数学の繋がりを重要視した常微分方程式に関する教材検討－生態系モデルに着目して－

    生天目悠也, 伊藤弘道

    日本数学教育学会 第5回春期研究大会  ( 横浜国立大学 )   2017.6 

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  • On crack problems for nonlinear elasticity （ある非線形弾性体におけるき裂問題について） International conference

    Hiromichi Itou

    保存則をもつ偏微分方程式に対する解の特異性および漸近挙動の研究  ( 京都大学数理解析研究所 )   2017.6 

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  • Nonlinear elasticity with limiting small strain for cracks subject to non-penetration International conference

    Hiromichi Itou

    International Conference on Elliptic and Parabolic Problems  ( Gaeta (イタリア) )   2017.5 

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  • ある非線形弾性体におけるき裂問題について

    伊藤弘道

    第63回岐阜数理科学セミナー  ( 岐阜大学サテライトキャンパス )   2017.3 

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  • Limiting small strain problem with contacting crack faces

    伊藤 弘道, V.A. Kovtunenko, K.R. Rajagopal

    日本応用数理学会 2017年 研究部会連合発表会  ( 電気通信大学 )   2017.3 

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  • On crack problems for nonlinear elasticity

    伊藤弘道

    Second Workshop on Mathematical Analysis on Nonlinear Phenomena  ( 慶應義塾大学 )   2017.1 

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  • On crack problems for nonlinear elasticity

    伊藤弘道

    Second Workshop on Mathematical Analysis on Nonlinear Phenomena  ( 慶應義塾大学 )   2017.1 

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  • On reconstruction of a welding area and the enclosure method International conference

    Hiromichi Itou

    DK Seminar  ( Alpen-Adria-Universität Klagenfurt, Klagenfurt )   2016.12 

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  • On reconstruction of a welding area and the enclosure method International conference

    Hiromichi Itou

    Group Seminar of IPMI  ( Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz )   2016.12 

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  • On reconstruction of a welding area and the enclosure method International conference

    Hiromichi Itou

    Seminar  ( Institute of Mathematics and Scientific Computing, University of Graz (グラーツ) )   2016.11 

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  • On Reconstruction of a Cavity In a Three Dimensional Linearized Viscoelasticity from Transient Boundary Data International conference

    Hiromichi Itou

    2nd East Asia Section of IPIA-Young Scholars Symposium  ( The National Center for Theoretical Sciences (NCTS)・Taipei )   2016.11 

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  • On a crack problem for a strain-limiting nonlinear elastic model International conference

    Hiromichi Itou

    MORE seminar "Modelling of materials - theory, model reduction and efficient numerical methods"  ( Charles University, Czech Republic )   2016.10 

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  • On asymptotic behavior of the displacement field near a tip of thin obstacles in linearized elasticity International conference

    Hiromichi Itou

    Fourth workshop on thin structures  ( ナポリ（イタリア）・Eremo SS. Salvatore )   2016.9 

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  • Examination teaching materials for the ordinary differential equation to increase learning motivation International conference

    Yuya Namatame, Hiromichi Itou

    2016 International Conference of East-Asian Association for Science Education (EASE2016 Tokyo)  ( Tokyo (Tokyo University of Science) )   2016.8 

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  • Development and practice of teaching materials of the cycloid for cooperation between subjects mathematics and physics International conference

    Daiki Inoue, Hiromichi Itou

    2016 International Conference of East-Asian Association for Science Education (EASE2016 Tokyo)  ( Tokyo (Tokyo University of Science) )   2016.8 

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  • ある非線形弾性体におけるき裂問題について

    伊藤弘道, V. A. Kovtunenko, K. R. Rajagopal

    日本数学会2016年度年会 函数方程式論分科会  ( つくば市・筑波大学 )   2016.3 

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  • On singularities in 2D linearized elasticity International conference

    Hiromichi Itou

    CoMFoS15: Mathematical Analysis of Continuum Mechanics and Industrial Applications  ( Kyushu University, Nishijin Plaza )   2015.11 

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  • 非線形弾性体の数学解析について

    伊藤弘道

    現象解析特別セミナー第8回  ( 東京理科大学 )   2015.9 

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  • The enclosure method for the evaluation of the spot welding area using a solution of the Laplace equation

    池畠優, 伊藤弘道, 笹本明

    日本数学会2015年度秋季総合分科会  ( 京都産業大学 )   2015.9 

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  • On reconstruction of a spot welding area in an electric conductive body International conference

    Hiromichi Itou

    The 8th International Congress on Industrial and Applied Mathematics  ( Beijing )   2015.8 

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  • On reconstruction of a welding area by means of the enclosure method using a single measurement International conference

    Hiromichi Itou

    Applied Inverse Problems(AIP2015)  ( Helsinki in Finland )   2015.5 

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  • 囲い込み法を用いた溶接部の再構成について

    伊藤弘道

    九州関数方程式セミナー  ( 福岡大学セミナーハウス )   2015.5 

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  • スポット溶接の精度評価の逆問題について

    池畠 優, 伊藤 弘道, 笹本 明

    日本応用数理学会 2015年 研究部会連合発表会  ( 明治大学 中野キャンパス )   2015.3 

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  • 囲い込み法を用いた溶接部の一組の観測データによる再構成について

    伊藤弘道

    微分方程式の逆問題とその周辺  ( 京都大学数理解析研究所 )   2015.1 

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  • On reconstruction of a spot welding area

    伊藤弘道

    第4回弘前非線形方程式研究会  ( 弘前大学 )   2014.12 

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  • On reconstruction of a spot welding area

    伊藤弘道

    第4回弘前非線形方程式研究会  ( 弘前大学 )   2014.12 

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  • 溶接の精度評価の逆問題について

    伊藤弘道

    広島微分方程式研究会  ( 広島大学 )   2014.10 

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  • On convergent series expansions of solutions of Navier’s equation near singular points International conference

    Hiromichi Itou

    Modeling, analysis and computing in nonlinear PDEs  ( Chateau Liblice, Czech Republic. )   2014.9 

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  • ON RECONSTRUCTION OF CAVITIES IN A THREE DIMENSIONAL LINEARIZED VISCOELASTICITY International conference

    Masaru Ikehata, Hiromichi Itou

    The 7th International Conference ”Inverse Problems: Modeling and Simulation”(IPMS-2014)  ( Fethiye, Turkey )   2014.5 

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  • 線形弾性体方程式の解の特異性について

    伊藤 弘道

    第１１６回神楽坂解析セミナー  ( 東京理科大学 )   2013.10 

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  • On convergent series expansions at a corner in linearized elasticity and Inverse problems International conference

    Hiromichi Itou

    JSA2013(Journées Singulières Augmentées 2013)  ( Rennes, France )   2013.8 

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  • ある３次元線形粘弾性体における空洞の再構成法について

    池畠 優, 伊藤 弘道

    第６２回理論応用力学講演会  ( 東京工業大学 )   2013.3 

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  • On convergent series expansions of solutions of the linearized elasticity equation near singular points

    伊藤 弘道

    Inverse problems of partial differential equations and related topics  ( 京都大学数理解析研究所 )   2012.11 

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  • On convergent series expansions of solutions of the linearized elasticity equation near singular points

    伊藤 弘道

    Inverse problems of partial differential equations and related topics  ( 京都大学数理解析研究所 )   2012.11 

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  • On reconstruction of a cavity in a linearized viscoelastic body from transient boundary data International conference

    Masaru Ikehata, Hiromichi Itou

    INVERSE AND ILL-POSED PROBLEMS OF MATHEMATICAL PHYSICS (The International Conference dedicated to the 80th anniversary of the birthday of Academician Mikhail Mikhailovich Lavrent'ev)  ( Novosibirsk, Russia )   2012.8 

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  • 粘弾性体における空洞の再構成について－リーズナブルな条件を求めて－

    伊藤 弘道

    現象解析特別セミナー  ( 茨城大学 )   2012.3 

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  • On asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity

    伊藤 弘道, A. M. Khludnev, E. M. Rudoy, 谷 温之

    日本応用数理学会  ( 九州大学 )   2012.3 

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  • On asymptotic behaviour at a tip of a rigid line inclusion in linearized elasticity

    伊藤 弘道, A. M. Khludnev, E. M. Rudoy, 谷 温之

    日本応用数理学会  ( 九州大学 )   2012.3 

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  • On reconstruction of a cavity in a linearized viscoelastic body from dynamical boundary data over a finite time interval International conference

    Hiromichi Itou

    ESF-JSPS Frontier Science Conference Series for Young Researchers (Mathematics for Innovation: Large and Complex Systems)  ( The Four Seasons Hotel Tokyo at Chinzan-so, Tokyo )   2012.2 

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  • On Convergent Series Expansions of Solutions of the Linearized Elasticity Equation near Singular Points International conference

    Hiromichi Itou

    ESF-JSPS Frontier Science Conference Series for Young Researchers (Mathematics for Innovation: Large and Complex Systems)  ( The Four Seasons Hotel Tokyo at Chinzan-so, Tokyo )   2012.2 

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  • On Convergent Expansions of Solutions of the Linearized Elasticity Equation near Singular Points International conference

    Hiromichi Itou

    9th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2011)  ( Halkidiki, Greece )   2011.9 

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  • On convergent expansions of solutions of the linearized elasticity equation near singular points International conference

    Hiromichi Itou

    6th International conference on MATHEMATICAL MODELING  ( Yakutsk, Russia )   2011.7 

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  • 線形弾性体方程式の解のき裂先端における特異性について

    伊藤 弘道

    九州関数方程式セミナー  ( 福岡大学 セミナーハウス )   2011.7 

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  • On Reconstruction of an Unknown Polygonal Cavity in a Linearized Elasticity with One Measurement International conference

    Hiromichi Itou

    International Conference on Inverse Problems (ICIP2010)  ( City University of Hong Kong )   2010.12 

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  • On a frictional interface crack problem between dissimilar linearized elastic media International conference

    Hiromichi Itou

    International Conference on Applied Mathematics and Informatics (ICAMI2010)  ( San Andres Island, Colombia )   2010.12 

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  • On a frictional interface crack problem between dissimilar linearized elastic media International conference

    Hiromichi Itou

    PERAMBULATION OF CONTINUUM MECHANICS (Meeting In Celebration of The Sixtieth Birthday of K. R. Rajagopal)  ( TEXAS A&M UNIVERSITY, U.S.A )   2010.11 

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  • On a frictional interface crack problem in dissimilar linearized elastic materials

    伊藤 弘道, V. A. Kovtunenko, 谷 温之

    日本数学会  ( 名古屋大学 )   2010.9 

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  • On a frictional interface crack problem in dissimilar linearized elastic materials

    伊藤 弘道, V. A. Kovtunenko, 谷 温之

    日本数学会  ( 名古屋大学 )   2010.9 

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  • On a frictional interface crack problem between dissimilar linearized elastic media

    伊藤 弘道, V. A. Kovtunenko, 谷 温之

    日本応用数理学会  ( 明治大学 )   2010.9 

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  • On a frictional interface crack problem between dissimilar linearized elastic media

    伊藤 弘道, V. A. Kovtunenko, 谷 温之

    日本応用数理学会  ( 明治大学 )   2010.9 

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  • Coulomb摩擦と非貫通条件を考慮した異種線形弾性体界面上のき裂問題について

    伊藤 弘道

    非線形解析セミナー  ( 慶應義塾大学 )   2010.6 

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  • On reconstruction of an unknown polygonal cavity in a linearized elastic body with one measurement International conference

    Hiromichi Itou

    5th International Conference IP:M&S (Inverse Problems: Modeling and Simulation)  ( Antalya, Turkey )   2010.5 

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  • Singularities of solutions of the linearized elasticity system near a corner or a crack tip and inverse problems

    伊藤 弘道

    微分方程式の総合的研究  ( 東京大学 )   2009.12 

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  • き裂先端や角における線形弾性体方程式の解の特異性と逆問題

    伊藤 弘道

    9th Workshop on Continuum Mechanics Focusing on Singularities(CoMFoS09)  ( 湘南国際村センター )   2009.11 

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  • 線形弾性体における多角形空洞の一組の観測データによる再構成について

    池畠 優, 伊藤 弘道

    日本応用数理学会  ( 大阪大学 )   2009.9 

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  • 線形弾性体における多角形空洞の一組の観測データによる再構成について

    伊藤 弘道

    第五回 非線型の諸問題  ( 長崎商工会議所 )   2009.9 

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  • On reconstruction of polygonal cavities in an elastic body with one measurement International conference

    Hiromichi Itou

    The 34th Sapporo Symposium on Partial Differential Equations  ( Hokkaido University )   2009.8 

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  • On reconstruction of an unknown cavity in an isotropic elastic body with one measurement

    池畠 優, 伊藤 弘道

    日本数学会  ( 東京大学 )   2009.3 

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  • On reconstruction of an unknown cavity in an isotropic elastic body with one measurement

    池畠 優, 伊藤 弘道

    日本数学会  ( 東京大学 )   2009.3 

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  • On reconstruction of an unknown polygonal cavity in an isotropic elastic body with one measurement

    池畠 優, 伊藤 弘道

    数理科学セミナー  ( 茨城大学 )   2009.3 

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  • 2次元線形弾性体における多角形空洞の凸包の一組の観測データによる再構成

    伊藤 弘道

    非線形解析セミナー  ( 慶應義塾大学 )   2008.12 

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  • On inverse crack problems in linearized elasticity International conference

    Hiromichi Itou

    8th Workshop on Continuum Mechanics Focusing on Singularities(CoMFoS08)  ( 京大会館 )   2008.10 

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  • 弾性体におけるき裂の逆問題と囲い込み法（池畠優（群馬大学）との共同研究）

    伊藤 弘道

    広島微分方程式研究会  ( 広島大学 )   2008.10 

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  • 再生核を用いた特異型積分方程式の近似解法について

    伊藤 弘道, 斎藤 三郎

    再生核の応用についての研究  ( 京都大学数理解析研究所 )   2008.9 

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  • 2次元非等方弾性体におけるき裂の逆問題（池畠優教授（群馬大学）との共同研究）

    伊藤 弘道

    非線形解析セミナー@大岡山  ( 東京工業大学 )   2008.7 

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  • Enclosure method and reconstruction of a linear crack in an elastic body International conference

    Masaru Ikehata, Hiromichi Itou

    6th International Conference on Inverse Problems in Engineering: Theory and Practice(ICIPE2008)  ( Dourdan (Paris), France )   2008.6 

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  • 2次元非等方弾性体におけるき裂の逆問題

    池畠 優, 伊藤 弘道

    数理科学セミナー  ( 茨城大学 )   2008.3 

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  • き裂先端における解の級数展開公式について

    池畠 優, 伊藤 弘道

    日本応用数理学会  ( 北海道大学 )   2007.9 

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  • A boundary value problem for an infinite elastic strip with a semi-infinite crack International conference

    Hiromichi Itou, Atusi Tani

    6th International Congress on Industrial and Applied Mathematics (ICIAM07)  ( Zürich University, Switzerland )   2007.7 

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  • On inverse crack problems in elastostatics International conference

    Masaru Ikehata, Hiromichi Itou

    6th International Congress on Industrial and Applied Mathematics (ICIAM07)  ( Zürich University, Switzerland )   2007.7 

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  • A boundary value problem for an infinite elastic strip with a semi-infinite crack International conference

    Hiromichi Itou, Atusi Tani

    The International Conference "Differential Equations, Theory of Functions, and Applications" Dedicated to the Centennial of Academician Ilia N. Vekua  ( Novosibirsk State University, Russia )   2007.5 

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  • Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data

    池畠 優, 伊藤 弘道

    日本数学会  ( 埼玉大学 )   2007.3 

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  • 弾性体における線状き裂の一組の観測データによる再構成

    伊藤 弘道

    第23回 ＮＡＰＲＡ（非線形解析プログラム研究会）合同分科会  ( 日本大学 )   2007.3 

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  • On inverse crack problems in elastostatics International conference

    Masaru Ikehata, Hiromichi Itou

    松山解析セミナー（第７回）  ( 愛媛大学 )   2007.2 

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  • Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data International conference

    Hiromichi Itou

    Workshop on Mathematical Analysis on Nonlinear Phenomena in honor of Professor Atusi Tani on the occasion of his 60th birthday  ( 慶應義塾大学 )   2006.12 

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  • 等方弾性体における線状き裂の一組の観測データによる再構成

    伊藤 弘道

    非線形解析セミナー  ( 慶應義塾大学 )   2006.11 

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  • 等方弾性体における線状き裂の一組の観測データによる再構成

    池畠 優, 伊藤 弘道

    日本応用数理学会  ( 筑波大学 )   2006.9 

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  • Reconstruction of a linear crack in an isotropic elastic body from a single set of measured data

    池畠 優, 伊藤 弘道

    数理科学セミナー  ( 茨城大学 )   2006.9 

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  • Existence of a weak solution in an infinite viscoelastic strip with a semi-infinite crack International conference

    Hiromichi Itou

    津波ワークショップ  ( 慶應義塾大学 )   2006.3 

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  • 等角写像を用いた屈折き裂問題の解法について

    伊藤 弘道

    等角写像論・値分布理論合同研究集会  ( 日本工業大学 )   2005.10 

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  • 屈折き裂問題の解の構成について

    伊藤 弘道

    日本応用数理学会  ( 東北大学 )   2005.9 

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  • Analytical and Numerical Solutions of Linear Singular Integral Equations

    伊藤 弘道, 斎藤 三郎

    日本数学会  ( 岡山大学 )   2005.9 

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  • On a problem for a kinked crack

    伊藤 弘道

    非線形解析セミナー@大岡山  ( 東京工業大学 )   2005.3 

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  • On a problem for a kinked crack

    伊藤 弘道

    非線形解析セミナー@大岡山  ( 東京工業大学 )   2005.3 

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  • On a problem for a kinked crack

    伊藤 弘道

    第２回 COE 破壊現象の数理ワークショップ'05  ( 慶應義塾大学 )   2005.3 

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  • On a problem for a kinked crack

    伊藤 弘道

    第２回 COE 破壊現象の数理ワークショップ'05  ( 慶應義塾大学 )   2005.3 

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  • 屈折亀裂の問題定式化と解法

    伊藤 弘道

    日本応用数理学会  ( 中央大学 )   2004.9 

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  • Existence of a weak solution in an infinite viscoelastic strip with a semi-infinite crack International conference

    Hiromichi Itou

    The Tenth International Conference on Hyperbolic Problems: Theory, Numerics and Applications  ( HOTEL HANKYU EXPO PARK )   2004.9 

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  • 屈折亀裂の問題定式化と解法

    伊藤 弘道

    数値解析・応用解析セミナー  ( 京都大学 )   2004.9 

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  • 屈折亀裂の問題定式化と解法

    伊藤 弘道

    数理科学セミナー  ( 茨城大学 )   2004.7 

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  • Mathematical analysis of fracture phenomena (the prediction problem of the crack path)

    伊藤 弘道

    九州関数方程式セミナー  ( 九州大学 )   2004.5 

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  • Boundary value problems and crack propagation in an infinite elastic strip with a semi-infinite crack

    伊藤 弘道

    Recent Topics in Nonlinear Partial Differential Equation  ( 広島大学 )   2004.1 

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  • Existence of a weak solution in an infinite viscoelastic strip with a semi-infinite crack

    伊藤 弘道, 谷 温之

    日本数学会  ( 千葉大学 )   2003.9 

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  • Existence of a weak solution in an infinite viscoelastic strip with a semi-infinite crack

    伊藤 弘道, 谷 温之

    日本数学会  ( 千葉大学 )   2003.9 

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  • A boundary value problem and crack propagation in an infinite (visco)elastic strip with a semi-infinite crack International conference

    Hiromichi Itou, Atusi Tani

    流体と気体の数学解析  ( 京都大学数理解析研究所 )   2003.7 

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  • A boundary value problem and crack propagation in an infinite (visco)elastic strip with a semi-infinite crack

    伊藤 弘道, 谷 温之

    数理科学セミナー  ( 茨城大学 )   2003.6 

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  • On crack propagation in an infinite elastic strip with a semi-infinite crack

    伊藤 弘道, 谷 温之

    日本数学会  ( 島根大学 )   2002.9 

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  • On crack propagation in an infinite elastic strip with a semi-infinite crack

    伊藤 弘道, 谷 温之

    日本数学会  ( 島根大学 )   2002.9 

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  • Boundary value problem in elastic media with a crack

    伊藤 弘道, 谷 温之

    日本数学会  ( 九州大学 )   2001.10 

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  • Boundary value problem in elastic media with a crack

    伊藤 弘道, 谷 温之

    日本数学会  ( 九州大学 )   2001.10 

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Awards

  • Top viewed article in 2023

    2025.4   Mathematical Methods in the Applied Sciences   A generalization of the Kelvin–Voigt model with pressure‐dependent moduli in which both stress and strain appear linearly

  • Top Downloaded Articles 2021

    2022.10   Mathematical Models and Methods in Applied Sciences   Lagrange multiplier approach to unilateral indentation problems: well-posedness and application to linearized viscoelasticity with non-invertible constitutive response

  • Top 10 Downloaded Articles 2021

    2022.8   Journal of Elasticity   On an Implicit Model Linear in Both Stress and Strain to Describe the Response of Porous Solids

  • Top Downloaded Articles 2021

    2022.1   Mathematical Models and Methods in Applied Sciences   Crack problem within the context of implicitly constituted quasi-linear viscoelasticity

  • Best papers of 2019 and 2020

    2020.10   Mathematical Models and Methods in Applied Sciences   Crack problem within the context of implicitly constituted quasi-linear viscoelasticity

  • The 11th Hukuhara Prize

    2019.12   Division of Functional Equations, The Mathematical Society of Japan  

  • The Best Presentation Award 2009

    2010.4   The Japan Society for Industrial and Applied Mathematics  

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Research Projects

  • Mathematical Analysis on problems under boundary conditions of friction type and its seismological application

    Grant number：24K06818  2024.4 - 2029.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Tokyo University of Science

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    Grant amount： \4680000 （ Direct Cost: \3600000 、 Indirect Cost： \1080000 ）

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  • Inverse problem theory for innovation of detection methods

    Grant number：23KK0049  2023.9 - 2028.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Fund for the Promotion of Joint International Research (International Collaborative Research)  Tokyo University of Science

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    Grant amount： \20280000 （ Direct Cost: \15600000 、 Indirect Cost： \4680000 ）

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  • Mathematical Analysis on dynamic rupture problems and its seismological application

    Grant number：18K03380  2018.4 - 2023.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Tokyo University of Science

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    Grant amount： \4550000 （ Direct Cost: \3500000 、 Indirect Cost： \1050000 ）

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  • 弾性構造物における破壊現象の数理解析とその応用 International coauthorship

    Grant number：JPJSBP120194824  2019.4 - 2022.3

    日本学術振興会  二国間交流事業（ロシアとの共同研究） 

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    Authorship：Principal investigator  Grant type：Competitive

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  • Mathematical modeling and analysis of discontinuous phenomena in continuum body

    Grant number：17H02857  2017.4 - 2021.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)  Kanazawa University

    KIMURA Masato

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    Grant amount： \17030000 （ Direct Cost: \13100000 、 Indirect Cost： \3930000 ）

    We conducted the following three research teams. Team 1 studied the contact and delamination phenomena, and the particle systems. Team 2 studied the fracture in gel and crack propagation models. Team 3 focused on the friction and the contact on the discontinuity surface and considered applications to the fault dynamics. The main results we obtained in this project are as follows. (1) mathematical analysis of the continuous limit problem and the boundary conditions for interacting particles [Team 1], (2) mathematical modeling of hyperbolic PDEs with delamination and their analysis [Team 1], (3) variational structures for a viscoelasticity model and a viscoelastic fracture model [Team 2], (4) mathematical analysis of a unidirectional evolution model related to the crack propagation [Team 2], (5) mathematical analysis of crack problems with the friction and the contact [Team 3], (6) mathematical analysis of the fault destruction.

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  • Mathematical analysis on Fracture phenomena and Aging problems in (visco)elasticity

    Grant number：26400178  2014.4 - 2019.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Tokyo University of Science

    Itou Hiromichi, IKEHATA masaru, KHLUDNEV A. M., KOVTUNENKO V. A., NAKAMURA gen, RAJAGOPAL K. R.

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    Grant amount： \4810000 （ Direct Cost: \3700000 、 Indirect Cost： \1110000 ）

    We studied elasticity models describing fracture phenomena and obtained the following results. First, in nonlinear elastic model called strain-limiting model, well-posedness of the generalized solution of a boundary value problem with a crack is shown. Second, we extended to the case of nonlinear viscoelastic model and similar results are obtained. Further, as an application of this study, we considered a reconstruction problem for cracks in two dimensional electrical conductive body by using electrical impedance tomography, and then we established a theoretical algorithm to extract cracks from measured data on the boundary.

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  • Mathematical Analysis of Free Boundary Problems in EMHD and Related Topics

    Grant number：26400176  2014.4 - 2017.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Keio University

    Tani Atusi, ITOH Sigeharu, TANAKA Naoto, ITOU Hiromichi, UMEHARA Morimichi

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    Grant amount： \3510000 （ Direct Cost: \2700000 、 Indirect Cost： \810000 ）

    Well-posedness of various nonlinear and free boundary problems in EMHD and its related fields was established mathematically. Some of the research results are as follows.
    (1) Free boundary problem for two-phase classical MHD for viscous and compressible fluids has been studied and proved to admit a unique local-in-time classical solution. (2) In the phenomenon of gas discharge the model system of PDEs due to Degon, Lucquin, Desreux and Morrow are investigated mathematically and established its unique solvability locally in time. (3) The fingering pattern of radially growing interface in a Hele-Shaw cell was shown in the framework of Hoelder spaces under surface tension effect on the interface between the displacing and displaced fluids taken into account through the parabolic regularization method. (4) Free boundary problem for two-phase, atmosphere and ocean, primitive equations has discussed and shown the existence of a unique strong solution locally in time.

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  • New development of the enclosure method for inverse obstacle scattering

    Grant number：25400155  2013.4 - 2017.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Hiroshima University

    Ikehata Masaru, ITOU HIROMICHI

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    Grant amount： \4680000 （ Direct Cost: \3600000 、 Indirect Cost： \1080000 ）

    First, inverse obstacle scattering problems of waves governed by the classical wave equation and Maxwell system under several boundary conditions have been considered by using the enclosure method in the finite time domain. Several formulas for extracting information about the location, shape and further the quantitative and qualitative state of the surface of the obstacle from the observed wave are given. Second, a new version of the time domain enclosure method using a single input has been discovered.
    Third, a method letting us know the estimation of the location together with the existence/nonexistence of unknown discontinuity embedded in a rough background medium from the observed wave has been introduced.

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  • Mathematical analysis of the non-Newtonian fluids flow

    Grant number：23654055  2011.4 - 2015.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research  Grant-in-Aid for Challenging Exploratory Research  Keio University

    TANI Atusi, IGUCHI Tatsuo, TAKAYAMA Masahiro, NDERA Takashi, ITOH Shigeharu, TANAKA Naoto, ITOU Hiromichi, UMEHARA Morimichi

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    Grant amount： \3510000 （ Direct Cost: \2700000 、 Indirect Cost： \810000 ）

    Well-posedness of nonlinear problems for various natural phenomena, especially of those described as non-Newtonian fluids flow was established mathematically. Some of research results are as follows.
    (1) For a non-Newtonian fluid flow, especially for the 2-dimensional flow of incompressible viscoelastic Maxwell media with a Jaumann corotational derivative in the rheological constitutive law we proved that the discontinuity can develop even from smooth initial data, and the stability of shocks in it without retardation. (2) An equilibrium problem for 2-dimensional homogeneous isotropic linearized elasticity with a rigid line inclusion was studied in both not delaminated and laminated cases, and investigated an asymptotic behavior of a solution near a tip of a rigid line inclusion. (3) The fingering pattern of radially growing interface in a Hele-Shaw cell was shown in the framework of weakly nonlinear analysis under the wetting layer effect of the displacing fluid taken into account.

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  • Elucidation of fracture phenomena from the viewpoint of singularity of solutions of partial differential equations at crack tips

    Grant number：23740101  2011 - 2014

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B) 

    ITOU HIROMICHI

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    Grant amount： \3510000 （ Direct Cost: \2700000 、 Indirect Cost： \810000 ）

    With application of fracture phenomena in mind, we studied the behavior of solutions of partial differential equations at crack tips. In a case of nonlinear equations we did not achieve anything new, but we found a toehold to solve the problem. In a case of boundary value problems in two dimensional elasticity with rigid line inclusions, we proved the existence and uniqueness of the solution and derived the convergent series expansion of the solution near the tip of the rigid inclusion. As an application of this study, we considered a reconstruction problem for cavities in three dimensional linear viscoelasticity, and we established a formula extracting three kinds of information about the unknown cavity from measured data on the boundary.

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  • Study on inverse problems for partial differential equations using the probe and enclosure methods

    Grant number：21540162  2009 - 2012

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Gunma University

    IKEHATA Masaru, ITOU Hiromichi

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    Grant amount： \4290000 （ Direct Cost: \3300000 、 Indirect Cost： \990000 ）

    The most representative results obtained in this study consists of two parts. The first one shows that the enclosure method using dynamical data overa finite time interval can be applied to several inverse problems for the heat and waveequations and visco-elastic system of equations in three dimensions. And also the result raises several problems to be solved. The second one is the finding of the idea thatthe logarithmic differential of the indicator function in the enclosure method appliedto inverse obstacle scattering problems governed by the Helmholtz equation yieldsinformation two times more than the original indicator function.

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  • Mathematical analysis of nonlinear elasticity for elucidation of fracture phenomena

    Grant number：21740091  2009 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)  Grant-in-Aid for Young Scientists (B)  Gunma University

    ITOU Hiromichi

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    Grant amount： \2210000 （ Direct Cost: \1700000 、 Indirect Cost： \510000 ）

    With application to fracture phenomena in mind, we studied mathematical analyses for the following nonlinear problems and obtained the results. First, in nonlinear elasticity which has a crack and the stress-strain relation is governed by power law, we showed a unique solvability of the weak solution for the boundary value problem. Second, we proved a solvability of the solution of a boundary value problem as a model of interfacial crack under the nonlinear condition (Coulomb friction law and non-penetration condition) between two bonded dissimilar linearized elastic media. Further, we investigated the behavior of the solution near the crack tip.

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  • Mathematics study of the continuum mechanics focusing on singularities

    Grant number：19340027  2007 - 2009

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)  Hiroshima Kokusai Gakuin University

    OHTSUKA Kohji, AZEGAMI Hideyuki, SUMI Yoichi, NARUKAWA Kimiaki, NISHIMURA Naoshi, HIROSE Sohichi, ITOU Hiromichi

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    Grant amount： \14950000 （ Direct Cost: \11500000 、 Indirect Cost： \3450000 ）

    Mainly on the mathematical modeling of fracture phenomena, we constructed the activity group CoMFoS (Continuum Mechanics Focusing on Singularities) in the Japan Society for Industrial and Applied Mathematics, and start the renewal of workshop. We get the results ; The modification of Griffith's energy balance theorem for the purpose of control theory on fracture phenomena, the proof of fundamental theorem in GJ-integral theory under nonlinearity of continuum mechanics, the application of GJ-integral method to shape optimization problem with Azegami's method, the construction of the Web site that carried contents of FreeFem++.

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  • Mathematical Analysis of various nonlinear problems for phenomena in continua

    Grant number：18340042  2006 - 2008

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B)  Keio University

    TANI Atusi, MAEJIMA Makoto, SHIMOMURA Shun, NODERA Takashi, TAMURA Akihisa, YOSHIZAWA Masatsugu, ISHIKAWA Shiro, IGUCHI Tatsuo, TAKAYAMA Masahiro, SUGIURA Toshihiko, ITOH Shigeharu, TANAKA Naoto, ITOU Hiromichi

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    Grant amount： \10090000 （ Direct Cost: \8500000 、 Indirect Cost： \1590000 ）

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  • Further development of the probe and enclosure methods

    Grant number：18540160  2006 - 2008

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Gunma University

    IKEHATA Masaru, TANUMA Kazumi, AMANO Kazuo, OHE Takashi, ITOU Hiromichi, TANUMA Kazumi, AMANO Kazuo, OHE Takashi

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    Grant amount： \3340000 （ Direct Cost: \2800000 、 Indirect Cost： \540000 ）

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  • き裂や角を含む領域における(粘)弾性体方程式の解析

    Grant number：18740067  2006 - 2007

    日本学術振興会  科学研究費助成事業 若手研究(B)  若手研究(B)  群馬大学

    伊藤 弘道

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    Grant amount： \2200000 （ Direct Cost: \2200000 ）

    1. き裂進展方向の予測問題を解析するために、屈折き裂を含む線形弾性板領域における定常問題の解の性質について考察した。この問題は特異型積分方程式で表現でき、その解の表現を得る事が重要である。そこで群馬大学齋藤三郎教授との共同研究によって一般の線形特異型積分方程式に対する近似解を構成する方法を提案し、その結果は共著論文としてInternational Journal of Applied Mathematics&Statisticsに掲載された。しかしこれによる問題解決には数値解析的手法が必要であり、現在研究中である。
    2. 破壊現象の理論的解析のために、Texas A & M UniversitvのK. R. Rajagopal教授と非線形弾性体モデルについての共同研究を行った。その結果、今まで理論的研究の主流であった線形弾性体よりも適用範囲の広い新しい非線形弾性体モデルについての知見を得た。そして、き裂を含む場合においてそのモデルの境界値問題に対する弱解の一意存在性を示した。さらにき裂先端における解の挙動についても考察しており、それらの結果について現在論文執筆中である。
    3. 非破壊検査に関わる境界値逆問題について、群馬大学池畠優教授の囲い込み法を援用し、考察した。具体的には、2次元非等方均質線形弾性体に含まれる線状き裂の位置を、物体にある表面力をかけ、その境界の一組の観測データから一意的に特定できる事を示した。その際、加える表面力については応力拡大係数がゼロでないという仮定よりもより一般的な枠組みで考察した。この結果は池畠氏との共著論文としてInverse Problemsに掲載された。またき裂だけでなく多角形の欠陥を再構成する問題についても研究中であり、現在までに多角形欠陥を含む領域における線形弾性体方程式の境界値問題の角の近傍における級数解を構成した。

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Committee Memberships

  • 2020.1 - Now

    Applications in Engineering Science   Editorial Board Member  

  • 2015.3 - Now

    The Japan Society for Industrial and Applied Mathematics   Organizer of the activity group Mathematical Aspects of Continuum Mechanics  

  • 2014.2 - Now

    Mathematical Inverse Problems   Editor  

  • 2013.3 - Now

    Mathematical notes of NEFU (North-Eastern Federal University in Yakutsk)   Editor  

  • 2010.3 - Now

    American Mathematical Society   Reviewer of Mathematical Reviews  

  • 2010.1 - Now

    日本応用数理学会   JSIAM Letters 編集委員  

  • 2026.5 - 2026.6

    12th International Conference "Inverse Problems: Modeling and Simulation"(IPMS 2026)   International Program Committee member  

  • 2024.5 - 2026.5

    The Eurasian Association on Inverse Problems (EAIP)   member of the Steering Committee  

  • 2025.4 - 2026.3

    日本応用数理学会   代表会員  

  • 2024.11 - 2025.9

    日本応用数理学会   2025年度年会 実行委員会 委員  

  • 2023.4 - 2025.3

    日本応用数理学会   代表会員  

  • 2021.4 - 2025.3

    東京理科大学   教職教育センター紀要編集委員会委員  

  • 2021.4 - 2025.3

    SUT Journal of Mathematics   Editor  

  • 2024.5 - 2024.6

    11th International Conference "Inverse Problems: Modeling and Simulation" (IPMS 2024)   International Program Committee member  

  • 2021.8 - 2023.8

    International Congress on Industrial and Applied Mathematics   Member of Local Scientific Program Committee  

  • 2022.5 　 　

    10th International Conference "Inverse Problems: Modeling and Simulation"(IPMS 2022)   International Program Committee member  

  • 2017.3 - 2021.12

    Inverse Problems in Science and Engineering (IPSE)   Associate Editor  

  • 2016.4 - 2021.3

    日本応用数理学会   代表会員  

  • 2017.8 - 2018.8

    第100回全国算数・数学教育研究（東京）大会   会計委員会委員  

  • 2017.8 - 2018.8

    第100回全国算数・数学教育研究（東京）大会   実行委員会事務局主任  

  • 2015.8 - 2018.8

    第100回全国算数・数学教育研究（東京）大会   講習委員会副委員長  

  • 2018.5 　 　

    9th International Conference "Inverse Problems: Modeling and Simulation"(IPMS 2018)   International Organizing Committee member  

  • 2015.8 - 2017.7

    第100回全国算数・数学教育研究（東京）大会   準備委員会事務局主任  

  • 2017.1 　 　

    RIMS conference "Inverse problems for partial differential equations and related areas"   Organizer  

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Academic Activities

  • Workshop for young scholars Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods -

    Role(s)： Planning, management, etc.

    2017.8 - Now

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  • Finland-Japan Workshop in Industrial and Applied Mathematics International contribution

    Role(s)： Planning, management, etc.

    Andreas Hauptmann, Takanori Ide, Hiromichi Itou, Matti Lassas, Lauri Oksanen, Samuli Siltanen  （ University of Helsinki, Finland ） 2024.8 　 　

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  • ミニシンポジウムM16. Inverse Problem Theory for Innovation of Detection Methods（11th International Conference ""Inverse Problems: Modeling and Simulation"）

    Role(s)： Planning, management, etc.

    Jérôme Fehrenbach, Hiromichi Itou, Yavar Kian, Victor A. Kovtunenko,  2024.5 - 2024.6

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  • ミニシンポジウム[01996]: Control and inverse problems on waves, oscillations and flows（10th International Congress on Industrial and Applied Mathematics (ICIAM2023)）

    Role(s)： Planning, management, etc.

    Hiromichi Itou, Atsushi Kawamoto, Yikan Liu, Hisashi Morioka  2023.8 　 　

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  • ミニシンポジウム[00085]: Singular Problems in Mechanics（10th International Congress on Industrial and Applied Mathematics (ICIAM2023)）

    Role(s)： Planning, management, etc.

    Victor Kovtunenko, Hiromichi Itou, Alexander Khludnev, Evgeny Rudoy  2023.8 　 　

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  • ミニシンポジウムM20: Inverse Obstacle and Control Problems in Mechanics（10th International Conference "Inverse Problems: Modeling and Simulation"）

    Role(s)： Planning, management, etc.

    Hiromichi Itou, Victor A. Kovtunenko, Gennadii V. Alekseev, Mikhail M. Lavrentiev, Jr.  2022.5 　 　

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  • ミニシンポジウムMS-ID8 Nonsmooth Variational Methods for PDEs and Applications in Mechanics（8th European Congress of Mathematics）

    Role(s)： Planning, management, etc.

    Victor A. Kovtunenko  2021.6 　 　

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  • 研究集会「Elastic and dissipative motions of curves and interfaces in continuum media」

    Role(s)： Planning, management, etc.

    東京理科大学総合研究院「数理解析連携研究部門」  2021.6 　 　

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  • ミニシンポジウムMS-72 Variational Analysis and Nonsmooth Optimization for Inverse Problems（AIP2019: Applied Inverse Problems conference）

    Role(s)： Planning, management, etc.

    Itou Hiromichi, Khan Akhtar, Resmerita Elena  2019.7 　 　

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  • 国際研究集会CoMFoS18: Mathematical Analysis of Continuum Mechanics II

    Role(s)： Planning, management, etc.

    日本応用数理学会 研究部会「連続体力学の数理」  2018.6 　 　

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  • ミニシンポジウムM2: Recent Developments in Inverse Boundary Value Problems and Applications（9th International Conference "Inverse Problems: Modeling and Simulation"）

    Role(s)： Planning, management, etc.

    Alexandre Kawano, Takashi Ohe, Hiromichi Itou,  2018.5 　 　

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  • 国際研究集会CoMFoS17: Mathematical Analysis of Continuum Mechanics

    Role(s)： Planning, management, etc.

    日本応用数理学会 研究部会「連続体力学の数理」  2017.9 　 　

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  • 国際研究集会CoMFoS15: Mathematical Analysis of Continuum Mechanics and Industrial Applications

    Role(s)： Planning, management, etc.

    日本応用数理学会 研究部会「連続体力学の数理」  2015.11 　 　

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