Faculty Profiles - MATSUYAMA Tokio

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

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

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

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

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

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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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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 L^p 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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L^p 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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Language：English Publisher：Gakkotosho

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

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

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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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Language：English Publisher：Gakkotosho

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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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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

Blowup rate for solutions to the Kirchhoff equation Invited

TOKIO MATSUYAMA

International Conference on Generalized Functions 2024.9

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Event date： 2024.9 　　

Language：English Presentation type：Oral presentation (general)

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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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Language：Japanese Presentation type：Public lecture, seminar, tutorial, course, or other speech

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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

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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L^p 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L^p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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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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Authorship：Principal investigator Grant type：Competitive

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

Tokyo Journal of Mathematics 副編集委員長
2015.4 - 2017.3

Tokyo Journal of Mathematics 編集委員
2010.4 - 2011.3

Tokyo Journal of Mathematics 編集委員