Updated on 2024/02/24

写真a

 
MATSUYAMA Tokio
 
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) ( 東京都立大学 )

  • 理学修士 ( 東京都立大学 )

Education

  • 1986.3
     

    Tokyo Metropolitan University   Graduate School, Division of Natural Science   Mathematics   master course   completed

Research History

  • 2000.4 - 2016.3

    早稲田大学教育学部数学科非常勤講師

  • 2012.2 - 2012.3

    ピサ大学数学教室客員研究員

  • 2011.4 -  

    Professor of Chuo University

  • 2002.4 - 2011.3

    東海大学理学部数学科教授

  • 2005.4 - 2006.3

    ピサ大学数学教室客員研究員

  • 1999.4 - 2004.3

    明治大学理工学部嘱託講師

  • 1998.4 - 2002.3

    東海大学理学部数学科助教授

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Professional Memberships

  • 日本数学会

Research Interests

  • Theory of Partial Differential Equations

Research Areas

  • Natural Science / Basic analysis  / Basic analysis

Papers

  • Bilinear estimates in Besov spaces generated by the Dirichlet Laplacian Reviewed

    Iwabuchi, Tsukasa, Matsuyama, Tokio, Taniguchi, Koichi

    J. Math. Anal. Appl.   494 ( 2 )   124640 - 124640   2021.2

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

    DOI: 10.1016/j.jmaa.2020.124640

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  • Besov spaces on open sets Reviewed

    T. Iwabuchi, T. Matsuyama, K. Taniguchi

    Bull. Sci. Math.   152   93 - 149   2019.2

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  • On the Gevrey well-posedness of the Kirchhoff equation Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    Journal d'Analyse Mathématique   137 ( 1 )   449 - 468   2019.2

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

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  • Boundedness of spectral multipliers for Schrödinger operators on open sets Reviewed

    Tsukasa Iwabuchi, Tokio Matsuyama, Koichi Taniguchi

    Revista Matemática Iberoamericana   34 ( 3 )   1277 - 1322   2018.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:European Mathematical Society  

    DOI: 10.4171/rmi/1024

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  • Almost global well-posedness of Kirchhoff equation with Gevrey data Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    COMPTES RENDUS MATHEMATIQUE   355 ( 5 )   522 - 525   2017.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER  

    The aim of this note is to present the almost global well-posedness result for the Cauchy problem for the Kirchhoff equation with large data in Gevrey spaces. We also briefly discuss the corresponding results in bounded and in exterior domains. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS.

    DOI: 10.1016/j.crma.2017.04.001

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  • Lp-boundedness of functions of Schrödinger operators on an open set of ℝd Reviewed

    Tsukasa Iwabuchi, Koichi Taniguchi

    New Trends in Analysis and Interdisciplinary Applications   307 - 312   2017

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

    DOI: 10.1007/978-3-319-48812-7_39

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  • The Kirchhoff equation with Gevrey data Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics   313 - 318   2017

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  • Global Well-Posedness of the Kirchhoff Equation and Kirchhoff Systems Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    ANALYTIC METHODS IN INTERDISCIPLINARY APPLICATIONS   116   81 - 96   2015

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:SPRINGER  

    This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data. Similar results will be obtained for the initial-boundary value problems in exterior domains with compact boundary. Also, the known results on large data problems will be reviewed together with open problems.

    DOI: 10.1007/978-3-319-12148-2_5

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  • Perturbed Besov spaces by a short-range type potential in an exterior domain

    Tokio Matsuyama

    Fourier Analysis, Pseudo-Differential Operators, Time-frequency Analysis and Partial Differential Equations, Trends in Math., M. Ruzhansky and V. Turunen eds.   285 - -309   2014.2

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  • Scattering for strictly hyperbolic systems with time-dependent coefficients Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    Mathematische Nachrichten   286 ( 11-12 )   1191 - 1207   2013.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Wiley-VCH Verlag  

    The present paper is devoted to finding conditions on the occurrence of scattering for strictly hyperbolic systems with time-dependent coefficients whose time-derivatives are in L1 in time. More precisely, it will be shown that the solutions are asymptotically free if the coefficients are stable in the sense that their improper Riemann integrals converge as t → ±∞, while each nontrivial solution with radially symmetric data is never asymptotically free provided that the coefficients are not stable as t → ±∞. As a by-product, wave and scattering operators can be constructed. An important feature is that assumptions on only one derivative of the coefficients are made so that the results would be applicable to the asymptotic behaviour of Kirchhoff systems. © 2013 WILEY-VCH Verlag GmbH &amp
    Co. KGaA, Weinheim.

    DOI: 10.1002/mana.201200095

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  • Global well-posedness of Kirchhoff systems Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    Journal de Mathématiques Pures et Appliquées (Liouville's journal)   100 ( 2 )   220 - 240   2013.7

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  • Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation Reviewed

    Tokio Matsuyama

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   62 ( 4 )   1167 - 1204   2010.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:MATH SOC JAPAN  

    The aim of this paper is to find a general class of data in which the global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation is assured. The result obtained in the present paper will be applied to the existence of scattering states. A class of weighted Sobolev spaces will be also presented in which the global well-posedness is assured. For this purpose, the method of generalized Fourier transforms is developed for some oscillatory integral associated with this equation. The crucial point is to obtain the resolvent expansion of the minus Laplacian around the origin in C, and the differentiability of the generalized Fourier transforms.

    DOI: 10.2969/jmsj/06241167

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  • ASYMPTOTIC INTEGRATION AND DISPERSION FOR HYPERBOLIC EQUATIONS Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    ADVANCES IN DIFFERENTIAL EQUATIONS   15 ( 7-8 )   721 - 756   2010.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:KHAYYAM PUBL CO INC  

    The aim of this paper is to establish time decay properties and dispersive estimates for strictly hyperbolic equations with homogeneous symbols and with time-dependent coefficients whose derivatives belong to L(1)(R). For this purpose, the method of asymptotic integration is developed for such equations and representation formulae for solutions are obtained. These formulae are analysed further to obtain time decay of L(p)-L(q) norms of propagators for the corresponding Cauchy problems. It turns out that the decay rates can be expressed in terms of certain geometric indices of the limiting equation and we carry out a thorough analysis of this relation. This provides a comprehensive view of asymptotic properties of solutions to time-perturbations of hyperbolic equations with constant coefficients. Moreover, we also obtain the time decay rate of the L(p)-L(q) estimates for equations of these kinds, so that the time well posedness of the corresponding nonlinear equations with additional semilinearity can be treated by standard Strichartz estimates.

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  • The Kirchhoff equation with global solutions in unbounded domains Reviewed

    Tokio Matsuyama

    Rendconti Istitute Matematica, University di Trieste   42 Suppliment   125 - 141   2010

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  • Time decay for hyperbolic equations with homogeneous symbols Reviewed

    Tokio Matsuyama, Michael Ruzhansky

    COMPTES RENDUS MATHEMATIQUE   347 ( 15-16 )   915 - 919   2009.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER  

    The aim of this Note is to present dispersive estimates for strictly hyperbolic equations with time dependent coefficients that have integrable derivatives. We will relate the time decay rate of L(p)-L(q) norms of solutions to certain geometric indices associated to the characteristics of the limiting equation. Results will be applied to the global solvability of Kirchhoff type equations with small data, and to the dispersive estimates for their solutions. To cite this article: T Matsuyama, M. Ruzhansky, C R. Acad. Sci. Paris, Ser. I 347 (2009). (c) 2009 Academie des sciences. Published by Elsevier Masson SAS. All fights reserved.

    DOI: 10.1016/j.crma.2009.06.010

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  • L-p-L-q estimates for wave equations and the Kirchhoff equation Reviewed

    Tokio Matsuyama

    OSAKA JOURNAL OF MATHEMATICS   45 ( 2 )   491 - 510   2008.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:OSAKA JOURNAL OF MATHEMATICS  

    The aim of this paper is to derive Lp-Lq estimates for strictly hyperbolic equations with time-dependent coefficients which are of Lipschitz class. Furthermore, Lp-Lq estimates tor Kirchhoff equation can be obtained by applying the Schauder-Tychonoff fixed point theorem.

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  • Dispersion and asymptotic profiles for Kirchhoff equations

    Tokio Matsuyama, Michael Ruzhansky

    Topics in contemporary differential geometry, complex analysis and mathematical physics   234 - 243   2007

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    Language:English   Publisher:World Scientific Publishing., Hackensack  

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  • Asymptotic behaviour for wave equation with time-dependent coefficients Reviewed

    Tokio Matsuyama

    Annali dell'Universita di Ferrara Sezione VII, Scienze Matematiche, Vol 52, No 2   52 ( 2 )   383 - 393   2006

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:UNIV FERRARA, DIPARTIMENTO MATEMATICA  

    We shall find asymptotic profiles for strictly hyperbolic equations with time-dependent coefficients which are of Lipschitz class and have some stability condition. More precisely, it will be shown that there exists a solution which is not asymptotically free provided that the coefficient tends slowly to some constant.

    DOI: 10.1007/s11565-006-0028-z

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  • Stabilization and L-p-L-q decay estimates Reviewed

    Tokio Matsuyama, Michael Reissig

    ASYMPTOTIC ANALYSIS   50 ( 3-4 )   239 - 268   2006

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

    The goal of the paper is to derive Strichartz estimates for solutions to wave equations with time-dependent coefficients belonging to C-r, 2 <= r <= 2n+1, and generating an anisotropic speed of propagation. A stabilization condition for the coefficients is introduced. This condition allows to show the Log-effect in L-p-L-q estimates and explains in this way the loss of decay.

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  • Asymptotic profiles for the Kirchhoff equation Reviewed

    Tokio Matsuyama

    RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI   17 ( 4 )   377 - 395   2006

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:EUROPEAN MATHEMATICAL SOC  

    The first aim of this paper is to find asymptotic profiles for the Kirchhoff equation. More precisely, it will be shown that there exists a small amplitude solution which is not asymptotically free. The second aim is to prove the existence of scattering states for small amplitude solutions with data belonging to H-sigma(p),H- p x H sigma((p)-1, p), where sigma(p) = n(2/p - 1) + 1, p is an element of [1, 2(n - 1)/(n + 1)) and n = 4.

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  • L-P-estimates for the wave equation with time-dependent dissipation Reviewed

    T Matsuyama

    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS   135 ( 2 )   393 - 412   2005

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ROYAL SOC EDINBURGH  

    We are interested in LP-estimates and scattering rates for the dissipative wave equation with time-dependent coefficients in an exterior domain outside a star-shaped obstacle. We want to notice the case that the support of dissipation expands strictly less than the wave speed. WE! develop a new cut-off method, which is time dependent. For this, we shall obtain the local energy decay over the time-dependent subdomain.

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  • The role of local energy decay in Lp estimates and scattering rates for the wave equation with time-dependent dissipation

    Tokio Matsuyama

    京都大学数理解析研究所講究録   1411   48 - 58   2005

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    Language:English   Publisher:京都大学  

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    Other Link: http://hdl.handle.net/2433/26192

  • SCATTERING STATES FOR THE NONLINEAR WAVE EQUATION WITH SMALL DATA Reviewed

    Tokio Matsuyama, Minoru Tanaka

    ADVANCES IN DIFFERENTIAL EQUATIONS   9 ( 7-8 )   721 - 744   2004.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:KHAYYAM PUBL CO INC  

    We investigate the energy nondecay and existence of scattering states for solutions to the initial-boundary-value problem for the nonlinear wave equation in exterior domains. When the space dimension is odd, the domain meets no geometrical condition. Otherwise, we assume that the obstacle is convex. For odd-dimensional general domains, taking into account the effective dissipation in trapping regions, we can derive the existence of scattering states. In particular, we can obtain also an L-2 bound of solutions. The method in deriving the energy nondecay is to utilize Huyghens' principle. For even-dimensional domains outside the convex obstacle, the asymptotics stated in the odd-dimensional case are also valid.

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  • Lp estimates and scattering rates for the wave equation with time-dependent dissipation

    Tokio Matsuyama

    Nonlinear partial differential equations and their applications, GAKUTO international series Mathematical Sciences and Applications, vol.20   159 - 174   2004

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  • Asymptotics for the nonlinear dissipative wave equation Reviewed

    T Matsuyama

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY   355 ( 3 )   865 - 900   2003

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    We are interested in the asymptotic behaviour of global classical solutions to the initial-boundary value problem for the nonlinear dissipative wave equation in the whole space or the exterior domain outside a star-shaped obstacle. We shall treat the nonlinear dissipative term like a(1)(1+\x\)(-delta)ut\(beta)u(t) (a(1), beta, delta > 0) and prove that the energy does not in general decay. Further, we can deduce that the classical solution is asymptotically free and the local energy decays at a certain rate as the time goes to infinity.

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  • Asymptotic behaviour of solutions for the nonlinear dissipative wave equation

    T Matsuyama

    PROGRESS IN ANALYSIS, VOLS I AND II   Ⅰ,Ⅱ   933 - 940   2003

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:WORLD SCIENTIFIC PUBL CO PTE LTD  

    We investigate the asymptotic behaviour of solutions to the initial-boundary value problem for the nonlinear dissipative wave equation in the whole space or the exterior domain outside a star-shaped obstacle. We shall treat the nonlinear dissipative term like a(1) (1 + \x\)(-delta)\u(t)\(beta)u(t) (a(1), beta, delta > 0) and prove that the energy does not in general decay. Further, we can deduce that the classical solution is asymptotically free and the local energy decays at a certain rate as t goes to infinity.

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  • Asymptotic behaviour of solutions for the wave equation with an effective dissipation around the boundary Reviewed

    T Matsuyama

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   271 ( 2 )   467 - 492   2002.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    We consider the initial-boundary value problem for the wave equation with a dissipation a(t, x)u(t) in an exterior domain, whose boundary meets no geometrical condition. We assume that the dissipation a(t, x)u(t) is effective around the boundary and a (t, x) decays as \x\ --> infinity. We shall prove that the total energy does not in general decay, and the solution is asymptotically free as the time goes to infinity. Further, we shall show that the local energy decays like O(t(-1)) (t --> infinity). (C) 2002 Elsevier Science (USA). All rights reserved.

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  • L2 behaviour of solutions to the linear heat and wave equations in exterior domains Reviewed

    Ryo Ikehata, Tokio Matsuyama

    Scientiae Mathematicae Japonicae   55 ( 1 )   33 - 42   2002

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Japanese Association of Mathematical Sciences  

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  • Remark on the L-2 estimates of the density for the compressible Navier-Stokes flow in R-3 Reviewed

    R Ikehata, T Kobayashi, T Matsuyama

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   47 ( 4 )   2519 - 2526   2001.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:PERGAMON-ELSEVIER SCIENCE LTD  

    We consider the uniform L-2-decay estimates of solutions near constant state (<(<rho>)over bar>(0), 0) for the Cauchy problem of the Compressible Navier-Stokes equations in R-3. We shall show that the L-2 norm of density rho (t, x) - <(<rho>)over bar>(0) decays like O(t(-1/4)) as t --> infinity for some initial data. In order to derive this L-2 decay rate, we shall use the L-2 decay estimates for the linear viscoelastic equation and L-p - L-q type estimates for the linearized compressible Navier-Stokes equations.

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  • Remarks on the behavior of solutions to the linear wave equations in unbounded domains. Reviewed

    Ryo Ikehata, Tokio Matsuyama

    Proceedings of the School of Science of Tokai University   36   1 - 13   2001

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:東海大学  

    Uniform L^2 decay of solutions for the linear dissipative wave equations will be given in a particular case when the initial data belongs to a manifold in L^2 (Ω)×L^2 (Ω). For this, we employ the modified method of Morawetz [7]. Furthermore, this technique will be applicable to obtain L^2 bound for the solutions to the free wave equations without any support compact condition of the initial data in exterior domains. As an application of this estimate, a simplified alternative proof for the local energy decay will be discussed. Finally, we shall remark the L^2 decay or bound under some additional conditions on the initial data, which is also an natural extension of the result of Kawashima et. al.[3]

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  • Quasilinear hyperbolic-hyperbolic singular perturbations with nonmonotone nonlinearity Reviewed

    T Matsuyama

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   35 ( 5 )   589 - 607   1999.3

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  • Global solutions to the initial-boundary value problem for the quasilinear wave equation with a weakly nonlinear dissipation. Reviewed

    Tokio Matsuyama

    Advance in Mathematical Analysis and Applications   9 ( 1 )   73 - 87   1999

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

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  • Global solutions to the initial-boundary value problem for the quasilinear bisco-elastic wave equation with a perturbation. Reviewed

    T. Matsuyama, R. Ikehara, M. Nakao

    Funkcialaj Ekvacioj   40 ( 2 )   293 - 312   1997

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:日本数学会函数方程式論分科会  

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  • Global existence and energy decay for a class of quasilinear wave equations with linear damping terms.

    Tokio Matsuyama

    Nonlinear waves, GAKUTO international series Mathematical Sciences and Applications, vol.10   293 - 298   1997

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  • Energy decay for the wave equations of Kirchholf type with linear damping terms. Reviewed

    Tokio Matsuyama, Ryo Ikehata

    Mathematical Japonicae   45 ( 2 )   315 - 355   1997

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Japanese Association of Mathematical Sciences  

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  • On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms Reviewed

    T Matsuyama, R Ikehata

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   204 ( 3 )   729 - 753   1996.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS  

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  • Singular limit of some quasilinear wave equations with damping and restoring terms Reviewed

    Tokio Matsuyama

    Tokyo Journal of Mathematics   19 ( 1 )   197 - 210   1996

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:TJM刊行会  

    A mixed problem for some hyperbolic equation with small parameter ε under the presence of a restoring term |u|αu and a reduced problem for a parabolic type are considered. Several ε weighted energy estimates can be obtained by the method of difference quotients. It is shown that the solution of the mixed problem converges, uniformly on any finite time interval, to the solution u of the problem for the parabolic equation in an appropriate Hilbert space as ε→0. © 1996 by the University of Notre Dame. All rights reserved.

    DOI: 10.3836/tjm/1270043229

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  • Singular limit of some quasilinear wave equations with damping terms. Reviewed

    Tokio Matsuyama

    Advances in Differential Equations   1 ( 2 )   151 - 174   1996

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

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  • Rapidly decreasing solutions and nonrelativistic limit of semilinear Dirac equations. Reviewed

    Tokio Matsuyama

    Reviews in Mathematial Physics   7 ( 2 )   243 - 267   1995.12

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

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  • A REMARK ON THE NONRELATIVISTIC LIMIT FOR SEMILINEAR DIRAC EQUATIONS Invited Reviewed

    T MATSUYAMA

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   25 ( 11 )   1139 - 1146   1995.12

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Books

  • 微分方程式を解く 解の存在・非存在

    松山 登喜夫( Role: Contributor)

    サイエンス社  2023.4 

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MISC

  • 書評:「フーリエ解析入門」(プリンストン解析学講義Ⅰ)

    松山登喜夫, 望月清

    数学通信   121 - 123   2010.5

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    Language:Japanese   Publishing type:Book review, literature introduction, etc.   Publisher:日本数学会  

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Presentations

  • Blow-up of the higher order energy of the solutions to the Kirchhoff equation Invited

    TOKIO MATSUYAMA

    More Anomalies in Partial Differential Equations  2023.9 

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    Event date: 2023.9    

    Language:English   Presentation type:Oral presentation (invited, special)  

    File: flyerconferenceBertinoro2023.pdf

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  • On wave equation outside trapping obstacles and local energy decay in odd space dimensions Invited International conference

    松山登喜夫

    International Conference on Generalized Functions  ( Vienna, Austria )   2022.9  Faculty of Mathematics, University of Vienna

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  • Long time existence of the Kirchhoff equation Invited International conference

    Tokio Matsuyama

    Dispersive and subelliptic PDEs, Centro di Ricerca Matematica, Ennio De Giorgi, Scuola Normale Superiore di Pisa  ( Pisa, Italy )   2020.2  Centro di Ricerca Matematica, Ennio De Giorgi, Scuola Normale Superiore

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  • Analytic well-posedness for wave equation with time-dependent coefficient, with application to the Kirchhoff equation Invited International conference

    Tokio Matsuyama

    Séminaires Equations aux Dérivées Partielles, Université de Franche-Comté, Laboratoire Mathématique de Besançon  ( Besançon in France )   2019.11  Université de Franche-Comté, Laboratoire Mathématique de Besançon

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  • Analytic well-posedness for wave equation with time-dependent coefficient, with application to the Kirchhoff equation Invited International conference

    Tokio Matsuyama

    Cardiff Analysis Seminar, School of Mathematics, Cardiff University  ( Cardiff in United Kingdom )   2019.10  School of Mathematics, Cardiff University

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  • Low frequency resolvent estimates for Dirichlet Laplacian on exterior domains Invited International conference

    Tokio Matsuyama

    INDAM Workshop, Anomalies in Partial Differential Equations, La Sapienza, Universitå di Roma  ( Roma, Italy )   2019.9  Istituto Nazionale di Alta Matematica

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  • Energy estimate for wave equation with bounded time-dependent coefficient Invited International conference

    Tokio Matsuyama

    12th Internatinal ISAAC Conference, University of Aveiro  ( Aveiro, Portugal )   2019.7  University of Aveiro

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  • Low frequency resolvent estimates for Dirichlet Laplacian on exterior domains Invited International conference

    Tokio Matsuyama

    45th International Conference, Applications of Mathematics in Engineering and Economics  ( Sozopol, Bulgaria )   2019.6  Faculty of Applied Mathematics and Informatics, Technical University of Sofia

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  • On the Gevrey well-posedness of the Kirchhoff equation

    International Conference on Generalized Functions GF2018, Dedicated to Professor Michael Oberguggenberger's 65th birthday  2018.8 

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  • On the Gevrey well-posedness of the Kirchhoff equation

    MicroLocal and Time Frequency Analysis 2018  2018.7 

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  • Kirchhoff 方程式の Cauchy 問題の可解性について

    神楽坂解析セミナー  2018.5 

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  • Kirchhoff 方程式の Cauchy 問題の可解性について

    岐阜数理科学セミナー  2018.5 

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  • Basov spaces generated by Dirichlet Laplacian

    Tsukasa Iwabuchi, Koichi Taniguchi

    Meeting of Mathematical Society of Japan  2018.3 

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  • Bilinear estimates in Besov spaces on a domain

    Tsukasa Iwabuchi, Koichi Taniguchi

    Meeting of Mathematical Society of Japan  2018.3 

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  • Besov spaces generated by the Schr ̈odinger operator

    Tsukasa Iwabuchi, Koichi Taniguchi

    Meeting of Mathematical Society of Japan  2018.3 

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  • Local energy decay estimates for wave equation on|rn|exterior domains

    11th ISAAC Congress in Växjö  2017.8 

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  • Local energy decay for wave equation on exterior domains

    東京理科大学理工学部談話会  2017.6 

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  • Local energy decay for wave equation on exterior domains

    Nagoya Differential Eqations seminar  2017.4 

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  • Decay estimates for wave equation with a potential on exterior domains

    International Conference on Generalised Functions|rn|GF2016  2016.9 

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  • Decay estimates for wave equation with a potential on exterior domains

    WinC2016 Wayamba International Conference  2016.8 

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  • Decay estimates for wave equation with a potential on exterior domains

    Mathematical Analysis for Stability in Nonlinear Dynamics in honor of Professor Vladimir Georgiev on his 60th birthday  2016.8 

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  • Gevrey class solutions of the Kirchhoff equation

    東海大学数学科・情報数理学科談話会  2016.1 

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  • Kirchhoff方程式のGevrey級解

    Michael Ruzhansky

    日本数学会秋季総合分科会 函数方程式論分科会  2015.9 

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  • Gevrey class solutions of the Kirchhoff equation

    Michael Ruzhansky

    10th International ISAAC Congress  2015.8 

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  • Kirchhoff方程式のGevrey級解

    南大阪応用数学セミナー  2015.7 

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  • Kirchhoff方程式のGevrey級解

    幾何と解析セミナー  2015.6 

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  • Kirchhoff方程式のGevrey級解

    第22回応用解析シンポジウ(於 熱海)  2015.3 

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  • Asymptotic integrations of ODE with application to the Kirchhoff equation

    実領域における常微分方程式の定性的理論とその応用  2014.11 

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  • キルヒホッフ方程式の時間大域解

    Encounter with Mathematics (Chuo University)  2014.9 

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  • Global existence for Kirchhoff systems

    Analysis seminar of Imperial College London  2014.3 

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    In this talk the global existence of Kirchhoff equation and systems is presented. Furthermore, some open problems are announced.

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  • Gevrey well-posedness of the Kirchhoff equation

    Michael Ruzhansky

    Seminar on Applied Analysis  2013.12 

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    This talk is about global Gevrey well-posedness of the Kirchhoff equation.

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  • Well-posedness of the Kirchhoff equation with small data

    Joint CRM-Isaac Conference on Fourier Analysis and Approximation Theory  2013.11 

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    I talked about a new result on global solutions of the Kirchhoff equation with small data in Sobolev spaces.

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  • Global well-posedness of the Kirchhoff equation and systems

    9th International ISAAC Congress  2013.8 

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  • Perturbed Besov spaces by short-range type potential in exterior domains

    調和解析駒場セミナー、東京大学数理科学研究科  2012.11 

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  • Strichartz estimates for hyperbolic systems with time-dependent coefficients

    Michael Ruzhansky

    International Conference on Fourier Analysis and Pseudo-Differential Operators  2012.6 

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  • Global solutions to Kirchhoff systems

    早稲田大学応用解析研究会  2011.11 

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  • Asymptotic properties for hyperbolic systems with time-dependent coefficients

    Michael Ruzhansky

    8th International ISAAC Congress, Moscow  2011.8 

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  • ポテンシャルを有する波動方程式の外部問題に対する分散型評価

    非線形解析セミナー@大岡山  2011.6 

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  • Dispersion for 3D wave equation with a potential in an exterior domain

    東海大学発展方程式シンポジウム  2011.3 

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  • Dispersion for 3D wave equation with a potential in an exterior domain

    Asymptotic Properties of Solutions to Hyperbolic Equations  2011.3 

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  • Dispersion for 3D wave equation with a potential in an exterior domain

    Microlocal Day #2  2010.12 

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  • Dispersion for 3D wave equation with a potential in an exterior domain

    Microlocal Day #2  2010.12 

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  • Dispersion for 3D wave equation with a potential in an exterior domain

    第104回学習院大学スペクトル理論セミナー  2010.11 

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  • Dispersion for 3D wave equation with a potential in an exterior domain

    第104回学習院大学スペクトル理論セミナー  2010.11 

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  • Dispension for 3D wave equation with a potential in exterior domains

    International Workshop on Global Properties of Partial Differential Equations on Manifolds  2010.9 

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  • Dispersion and Strichartz estimates for wave equation with a potential in exterior domains

    International Workshop "Fourier Analysis and Partial Differential Equations"  2010.6 

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  • Dispension for 3D wave equation with a potential in exterior domains

    大阪大学微分方程式セミナー  2010.6 

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  • Global wellposedness for the exterior initial-boundary value problem to the Kirchhoff equation

    偏微分方程式の諸問題  2009.11 

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  • Kirchhoff方程式の外部問題

    応用解析研究会500回記念講演会  2009.11 

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  • Kirchhoff equation in an exterior domain

    International Conference on Generalized Functions  2009.9 

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  • Strichartz estimates for hyperbolic equations in an exterior domain

    7th International ISAAC Congress  2009.7 

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  • Global wellposedness for the exterior initial-boundary value problem to the Kirchhoff equation

    望月清先生退職記念研究集会  2009.3 

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  • Geometrical optics for hyperbolic equations

    Michael Ruzhansky

    Decay and regularity for solutions of differential equations and dynamical systems  2008.9 

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  • Scattering for the Kirchhoff equation with nonlinear perturbations

    Michael Ruzhansky

    Function Spaces and Partial Differential Equations  2008.2 

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  • Dispersion for the Kirchhoff equations

    Issac Congress 2007, International Society for Analysis, its Applications and Computations  2007.8 

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  • Global solvability to Kirchhoff equations of higher order

    Interpaly between pseudo-differential operators and PDEs  2007.1 

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  • Asymptotic profiles for Kirchhoff equation

    第24回九州における偏微分方程式研究集会  2007.1 

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  • Asymptotic profiles for Kirchhoff equation

    広島数理解析セミナー  2006.11 

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  • Asymptotic profiles for Kirchhoff equation

    Workshop on Complex Structures and Vector Fields  2006.8 

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  • Asymptotic analysis for Kirchhoff equation

    AIMS' Sixth International Conference on Dyn. Systems, Diff. Equations and Applications, American Institute of Mathematical Sciences, Poitier(France)  2006.6 

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  • Asymptotic behaviours for Kirchhoff equation

    Nonlinear Elliptic and Parabolic Problems II  2005.9 

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  • Asymptotic behaviours for Kirchhoff equation

    Issac Congress 2005  2005.7 

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  • Asymptotics for wave equations with time-dependent coefficients

    Hyperbolic Systems, Memory of Stefano  2005.6 

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  • Asymptotics for wave equations with time-dependent coefficients

    Fourier Analysis and Hyperbolic PDEs  2005.5 

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  • Lp estimates for the wave equation with time dependent dissipation

    The Fourth World Congress of Nonlinear Analysts  2004.7 

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  • 時間に依存する摩擦の効果と波動方程式の局所エネルギーの減衰評価について

    エネルギーの評価から見た波動方程式の研究  2004.5 

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  • 時間に依存した摩擦項をもつ波動方程式のLp評価

    2004年度日本数学会年会函数方程式論分科会  2004.3 

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  • Asymptotics for the Nonlinear Wave Equation with small data

    German-Japanese Symposium on Qualitative Properties of Solutions to Hyperbolic and Schrodinger Equations  2003.6 

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  • 非線形摩擦項をもつ波動方程式の解の漸近挙動について

    日本数学会年会  2002.3 

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  • Asymptotic behaviour of solutions to the nonlinear dissipative wave equations

    3rd International ISAAC Congress  2001.8 

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  • Local energy decay for the nonlinear dissive wave equation in an exterior domain

    神楽坂解析セミナー  2001.4 

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  • 境界の近傍に摩擦が局在した波動方程式の外部問題における解の漸近挙動

    日本数学会2000年度年会函数方程式論分科会  2001.3 

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  • 外部領域における非線型波動方程式の古典解とその挙動

    函数方程式セミナー  2000.5 

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    In this talk we presented asymptotic behavior for classical solutions to wave equation with nonlinear dissipative term in an exterior domain.

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  • Global solutions to the initial-boundary value problem for the quasilinear visco-elastic wave equation with a perturbation

    池畠良, 中尾傎宏

    解析学火曜セミナー  1998.5 

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Research Projects

  • 特異積分と関数空間の研究(多重線形作用素の理論の深化)

    Grant number:22K03393  2022.4 - 2025.3

    日本学術振興会  科学研究費助成事業  基盤研究(C)  東海大学

    古谷 康雄, 澤野 嘉宏, 松山 登喜夫

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    Grant amount: \1950000 ( Direct Cost: \1500000 、 Indirect Cost: \450000 )

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  • Global analysis of the Kirchhoff equation

    2018.4 - 2023.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    松山登喜夫

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount: \3900000

    Global existence of the Kirchhoff equation with Gevrey data

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  • A study of multilinear operators

    Grant number:19K03571  2019.4 - 2022.3

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

    Furuya Yasuo

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    Grant amount: \2340000 ( Direct Cost: \1800000 、 Indirect Cost: \540000 )

    We study multilinear singular integral operators; the bilinear and trilinear Hilbert transform and fractional integral operators. We obtain weighted Stein-Weiss inequalities for multilinear fractional integrals.

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  • A study of singular integral operators

    Grant number:15K04938  2015.4 - 2018.3

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

    Furuya Yasuo

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

    We consider the boundedness of singular integral operators. In particular we study multilinear fractional operators and obtain the strong type estimates on product of Lebesgue spaces at critical indices. We also improve bilinear Stein-Weiss inequality.

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  • Global theory of the Kirchhoff equation

    2015.4 - 2018.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C) 

    松山登喜夫

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    Grant amount: \2990000

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  • A study of singular integrals and function spaces

    Grant number:24540194  2012.4 - 2015.3

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

    FURUYA Yasuo, SAWANO Yoshihiro, MATSYAMA Tokio

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

    We prove the boundedness of multilinear fractional integral operators on product of Herz spaces. We also consider supercritical cases. We introduce new function spaces called B_sigma spaces which unify Morrey spaces and Herz spaces, and prove the boundedness of the Hardy-Littlewood maximaloperator,singular integral operators and fractional integral operators on this space. We obtain the boounded of fractional integral operators on weighted Morrey space. Our result generalizes both Muckenhoupt-Wheeden inequality and Adams inequality.

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  • Dispersion for Kirrchhoff equation

    2012.4 - 2014.3

    松山登喜夫

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount: \730000

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  • キルヒホッフ方程式の散逸評価

    2009.4 - 2014.3

    文部科学省  科学研究費助成事業 基盤研究(C) 

    松山 登喜夫

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    Authorship:Principal investigator  Grant type:Competitive

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

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  • Study of singular integrals and function spaces

    Grant number:21540199  2009 - 2011

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

    FURUYA Yasuo, NARASAKI Takashi, MATSUYAMA Tokio

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    Grant amount: \3250000 ( Direct Cost: \2500000 、 Indirect Cost: \750000 )

    We study boundedness of generalized singular integral operators on several function spaces, in particular, on Hardy space, Morrey space and Herz space. We also study multilinear singular interals and weighted estimates.

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  • Nonlinear hyperbolic-parabolic singular perturbation

    Grant number:19540199  2007 - 2008

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

    YAMAZAKI Taeko

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    Grant amount: \1430000 ( Direct Cost: \1100000 、 Indirect Cost: \330000 )

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  • Almost periodic oscillations of linear and nonlinear hyperbolic equations

    Grant number:18540220  2006 - 2008

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

    YAMAGUCHI Masaru, MATSUYAMA Tokio, NARAZAKI Takashi, TANAKA Minoru

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    Grant amount: \4030000 ( Direct Cost: \3400000 、 Indirect Cost: \630000 )

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  • 波動方程式の漸近挙動に関する研究

    Grant number:16540205  2004.4 - 2005.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C)  Grant-in-Aid for Scientific Research (C)  Tokai University

    松山登喜夫

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    Grant amount: \800000

    外部領域における波動方程式において、摩擦の効果が時間とともに広がっていくときのエネルギー非減衰と散乱問題を解明した。また、境界の近傍に摩擦効果がある場合も同様な結果が得られている。

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  • The global behavior of solutions of evolution equations in noncylindrical domain with time-moving boundaries

    Grant number:15540213  2003 - 2005

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

    YAMAGUCHI Masaru, AKAMATSU Toyohiro, ITOH Tatsuo, TANAKA Minoru, MATSUYAMA Tokio

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    Grant amount: \3600000 ( Direct Cost: \3600000 )

    1) Let the space dimension be 1 to 5. Consider nonlinear sphere-symmetric autonomous wave equations in ball. We showed that the equations have infinitely many time-periodic solutions. In the proof we used the Diophantine inequalities on the eigenvalues of Laplacian and the periods. To this end we studied in detail numerical properties of the zero points of the Bessel functions, using the asymptotic expansions of the zero points.
    2) We considered IBVP for linear equations of heavy suspended string. Assume that time-quasiperiodic force works to the string. We assume the general Diophantine conditions on the eigenvalues of the string operator and the quasi perios Then we completely made clear the strunture of almost periodic structure of the solutions of IBVP. To show this statement, we defined well-matched function spaces, solved the eigenfunction problem in these function spaces and constructed the spectral theory.
    3) We considered BVP for nonlinear sphere-symmetric wave equations in ball with periodically moving boundaries. Then we showed the existence of periodic solutions of the BVP.
    4) The following theorem on the geodesics on manifolds is proved by M.Tanaka.
    Theorem : Let M be a real analytic Riemaniann manifold homeomorphic to a 2-sphere. If the Gaussian curvature of M is positive, then the conjugate locus of each point consists of a single point or has at least 4 cusps.

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  • Research on the Behavior of Solutions Evolution Equations in Time-Almost Periodic Noncylindrical Domains

    Grant number:12640220  2000 - 2002

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

    YAMAGUCHI Masaru, MATSUYAMA Tokio, TANAKA Minoru, AKAMATSU Toyohiro

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    Grant amount: \3600000 ( Direct Cost: \3600000 )

    In this project we dealt with linear and nonlinear wave equations in noncylindrical domain periodic or quasiperiodic in time. We studied the qualitative behavior of solutions of the initial boundary value problems (IBVP) and the boundary value problems (BVP). Our results are as follows.
    (1) We considered BVP for 1-D nonlinear wave equations in time-periodic noncylindrical domains. If the nonlinear forcing term, the boundary functions and the boundary data are periodic in time with same period, BVP have time-periodic solutions. This problem had been regarded as one of the difficult problems.
    (2) We considered IBVP for 1-D linear wave equations in time-quasiperiodic noncylindrical domains. The nonhomogeneous terms of the equations and the boundary data are also time quasiperiodic. As we showed in the previous Research Project, the solutions are generally almost periodic in time, hence bounded in time. We studied this phenomena more deeply, and found that there exist solutions which are the superpositions of time-unbounded waves.
    (3) We considered IBVP for 3-D radially symmetric linear wave equations in time-quasiperiodic noncylindrical domains whose space-domains are surrounded by two balls. We showed that the solutions are generally almost periodic in time.
    (4) We considered BVP for 3-D radially symmetric nonlinear wave equations in time-periodic noncylindrical domains whose space-domains are balls. Under the similar assumptions to those of (1) BVP have time-periodic solutions. The results seem to be interesting.
    In order to solve the problems, we developed some useful method. This method consists of a transformation of BVP for wave equations to some functional equations and domain transformations that transform the noncylindrical domains to cylindrical domains. The former was established by M. Yamaguchi and the latter by M. Yamaguchi and H. Yoshida. This method is based on the Reduction Theorems by M. Herman and J. Yoccoz in periodic case and by M. Yamaguchi in quasiperiodic case.

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  • 外部領域における波動方程式の解の漸近挙動

    Grant number:11640213  1999.4 - 2000.3

    文部科学省  科学研究費補助金(日本学術振興会・文部科学省)-基盤研究(C)  Grant-in-Aid for Scientific Research (C)  TOKAI UNIVERSITY

    松山登喜夫

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount: \2800000

    線形および非線形摩擦項を有する外部領域における解のエネルギー減衰・非減衰を明らかにした。エネルギーが減衰しない場合、散乱状態の存在を示した。

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Committee Memberships

  • 2020.4 - 2024.3

    Tokyo Journal of Mathematics   編集委員長  

  • 2017.4 - 2019.3

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