Updated on 2021/12/26

写真a

 
TANIGUCHI Masaharu
 
Organization
Research Institute for Interdisciplinary Science Professor
Position
Professor
External link

Degree

  • Master of Engineering

  • Doctor

Research Areas

  • Natural Science / Mathematical analysis

Education

  • The University of Tokyo   大学院数理科学研究科   数理科学

    - 1993.9

      More details

    Country: Japan

    researchmap

  • The University of Tokyo    

    - 1993

      More details

  • The University of Tokyo   理学部   数学科

    - 1989

      More details

    Country: Japan

    researchmap

Research History

  • Okayama University   Research Institute for Interdisciplinary Science   Professor

    2016.4

      More details

  • Okayama University   Graduate School of Natural Science and Technology   Professor

    2013.4 - 2015.3

      More details

  • Tokyo Institute of Technology   大学院情報理工学研究科   Associate Professor

    2007.4 - 2012.3

      More details

  • Tokyo Institute of Technology   Graduate School of Information Science and Engineering   Associate Professor (as old post name)

    2001.3 - 2007.4

      More details

  • Tokyo Institute of Technology   Graduate School of Information Science and Engineering   Lecturer

    1996.10 - 2001.2

      More details

  • :Tokyo Institute of Technology

    1996 - 2001

      More details

  • Kyoto University   数理解析研究所   Research Assistant

    1993.10 - 1996.9

      More details

▼display all

Professional Memberships

Committee Memberships

  • Department of Mathematics   Chairman  

    2020.4 - 2021.3   

      More details

  • Division of Interdisciplinary Science   Chairman  

    2019.4 - 2021.3   

      More details

  • 日本数学会   全国区代議員(評議員)  

    2016.3 - 2017.2   

      More details

    Committee type:Academic society

    researchmap

  • 日本数学会   代議員  

    2008   

      More details

    Committee type:Academic society

    日本数学会

    researchmap

  • 日本応用数理学会   学会誌「応用数理」編集委員  

    2006.4 - 2010.3   

      More details

    Committee type:Academic society

    日本応用数理学会

    researchmap

 

Papers

  • Traveling fronts in balanced bistable reaction-diffusion equations Invited Reviewed

    Masaharu Taniguchi

    Advanced Studies in Pure Mathematics   85   417 - 428   2020.12

     More details

    Authorship:Lead author   Language:English   Publishing type:Research paper (international conference proceedings)  

    researchmap

  • Existence and stability of stationary solutions to the Allen--Cahn equation discretized in space and time Reviewed

    Amy Poh Ai Ling, Masaharu Taniguchi

    62   197 - 210   2020.1

     More details

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

    researchmap

  • Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations Invited Reviewed

    Masaharu Taniguchi

    Discrete and Continuous Dynamical Systems. Series A   40 ( 6 )   3981 - 3995   2020

     More details

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

    researchmap

  • Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations Reviewed

    Masaharu Taniguchi

    Annales de l'Institut Henri Poincare C, Analyse Non Lineaire   36 ( 7 )   1791 - 1816   2019

     More details

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

    DOI: 10.1016/j.anihpc.2019.05.001

    researchmap

  • Convex compact sets in RN-1 give traveling fronts of cooperation-diffusion systems in R-N Reviewed

    Masaharu Taniguchi

    JOURNAL OF DIFFERENTIAL EQUATIONS   260 ( 5 )   4301 - 4338   2016.3

     More details

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

    This paper studies traveling fronts to cooperation diffusion systems in R-N for N >= 3. We consider (N - 2)-dimensional smooth surfaces as boundaries of strictly convex compact sets in RN-1, and define an equivalence relation between them. We prove that there exists a traveling front associated with a given surface and show its stability. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation. (C) 2015 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jde.2015.11.010

    Web of Science

    researchmap

  • AN (N-1)-DIMENSIONAL CONVEX COMPACT SET GIVES AN N-DIMENSIONAL TRAVELING FRONT IN THE ALLEN-CAHN EQUATION Reviewed

    Masaharu Taniguchi

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   47 ( 1 )   455 - 476   2015

     More details

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

    This paper studies traveling fronts to the Allen-Cahn equation in RN for N >= 3. Let (N - 2)-dimensional smooth surfaces be the boundaries of compact sets in RN-1 and assume that all principal curvatures are positive everywhere. We define an equivalence relation between them and prove that there exists a traveling front associated with a given surface and that it is asymptotically stable for given initial perturbation. The associated traveling fronts coincide up to phase transition if and only if the given surfaces satisfy the equivalence relation.

    DOI: 10.1137/130945041

    Web of Science

    researchmap

  • NON-EXISTENCE OF LOCALIZED TRAVELLING WAVES WITH NON-ZERO SPEED IN SINGLE REACTION-DIFFUSION EQUATIONS Reviewed

    Yong Jung Kim, Wei-Ming Ni, Masaharu Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   33 ( 8 )   3707 - 3718   2013.8

     More details

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

    Assume a single reaction-diffusion equation has zero as an asymptotically stable stationary point. Then we prove that there exist no localized travelling waves with non-zero speed. If [lim inf(vertical bar x vertical bar -> infinity) u(x), lim sup(vertical bar x vertical bar -> infinity) u(x)] is included in an open interval of zero that does not include other stationary points, then the speed has to be zero or the travelling profile u has to be identically zero.

    DOI: 10.3934/dcds.2013.33.3707

    Web of Science

    researchmap

  • TRAVELING FRONTS OF PYRAMIDAL SHAPES IN COMPETITION-DIFFUSION SYSTEMS Reviewed

    Wei-Ming Ni, Masaharu Taniguchi

    NETWORKS AND HETEROGENEOUS MEDIA   8 ( 1 )   379 - 395   2013.3

     More details

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

    It is well known that a competition-diffusion system has a one-dimensional traveling front. This paper studies traveling front solutions of pyramidal shapes in a competition-diffusion system in R-N with N >= 2. By using a multi-scale method, we construct a suitable pair of a supersolution and a subsolution, and find a pyramidal traveling front solution between them.

    DOI: 10.3934/nhm.2013.8.379

    Web of Science

    researchmap

  • MULTI-DIMENSIONAL TRAVELING FRONTS IN BISTABLE REACTION-DIFFUSION EQUATIONS Reviewed

    Masaharu Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   32 ( 3 )   1011 - 1046   2012.3

     More details

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

    This paper studies traveling front solutions of convex polyhedral shapes in bistable reaction-diffusion equations including the Allen-Cahn equations or the Nagumo equations. By taking the limits of such solutions as the lateral faces go to infinity, we construct a three-dimensional traveling front solution for any given g is an element of C-infinity (S-1) with min(0 <=theta <= 2 pi) g(theta) = 0.

    DOI: 10.3934/dcds.2012.32.1011

    Web of Science

    researchmap

  • TRAVELING FRONTS IN PERTURBED MULTISTABLE REACTION-DIFFUSION EQUATIONS Reviewed

    Masaharu Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   31   1368 - 1377   2011.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:AMER INST MATHEMATICAL SCIENCES-AIMS  

    In this paper we study the existence and non-existence of traveling front solutions in multistable reaction-diffusion equations. If this equation has a traveling front solution, a perturbed equation also has a traveling front solution. We study how the speed and the traveling profile depend on nonlinear terms.

    Web of Science

    researchmap

  • Multi-dimensional pyramidal travelling fronts in the Allen-Cahn equations Reviewed

    Yu Kurokawa, Masaharu Taniguchi

    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS   141   1031 - 1054   2011

     More details

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

    We study travelling-front solutions of pyramidal shapes in the Allen-Cahn equation in R(N) with N >= 3. It is well known that two-dimensional V-form travelling fronts and three-dimensional pyramidal travelling fronts exist and are stable. The aim of this paper is to show that for N >= 4 there exist N-dimensional pyramidal travelling fronts. We construct a supersolution and a subsolution, and find a pyramidal travelling-front solution between them. For the construction of a supersolution we use a multi-scale method.

    Web of Science

    researchmap

  • The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations Reviewed

    Masaharu Taniguchi

    JOURNAL OF DIFFERENTIAL EQUATIONS   246 ( 5 )   2103 - 2130   2009.3

     More details

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

    This paper studies the uniqueness and the asymptotic stability of a pyramidal traveling front in the three-dimensional whole space. For a given admissible pyramid we prove that a pyramidal traveling front is uniquely determined and that it is asymptotically stable under the condition that given perturbations decay at infinity. For this purpose we characterize the pyramidal traveling front as a combination of planar fronts on the lateral surfaces. Moreover we characterize the pyramidal traveling front in another way, that is, we write it as a combination of two-dimensional V-form waves on the edges. This characterization also uniquely determines a pyramidal traveling front. (c) 2008 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jde.2008.06.037

    Web of Science

    researchmap

  • Stability of Planar Waves in the Allen-Cahn Equation Reviewed

    Hiroshi Matano, Mitsunori Nara, Masaharu Taniguchi

    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS   34 ( 9 )   976 - 1002   2009

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:TAYLOR & FRANCIS INC  

    We study the asymptotic stability of planar waves for the Allen-Cahn equation on n, where n epsilon 2. Our first result states that planar waves are asymptotically stable under anypossibly largeinitial perturbations that decay at space infinity. Our second result states that the planar waves are asymptotically stable under almost periodic perturbations. More precisely, the perturbed solution converges to a planar wave as t. The convergence is uniform in n. Lastly, the existence of a solution that oscillates permanently between two planar waves is shown, which implies that planar waves are not asymptotically stable under more general perturbations.

    DOI: 10.1080/03605300902963500

    Web of Science

    researchmap

  • The condition on the stability of stationary lines in a curvature flow in the whole plane

    Mitsunori Nara, Masaharu Taniguchi

    JOURNAL OF DIFFERENTIAL EQUATIONS   237 ( 1 )   61 - 76   2007.6

     More details

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

    The long time behavior of a curve in the whole plane moving by a curvature flow is studied. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. Here the initial curves are given by bounded functions on the x-axis. It is proved that the solution converges uniformly to the solution of the Cauchy problem of the heat equation with the same initial value. The difference is of order O (t(-1/2)) as time goes to infinity. The proof is based on the decay estimates for the derivatives of the solution. By virtue of the stability results for the heat equation, our result gives the sufficient and necessary condition on the stability of constant solutions that represent stationary lines of the curvature flow in the whole plane. (C) 2007 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jde.2007.02.012

    Web of Science

    researchmap

  • Traveling fronts of pyramidal shapes in the Allen-Cahn equations

    Masaharu Taniguchi

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   39 ( 1 )   319 - 344   2007

     More details

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

    This paper studies pyramidal traveling fronts in the Allen-Cahn equation or in the Nagumo equation. For the nonlinearity we are concerned mainly with the bistable reaction term with unbalanced energy density. Two-dimensional V-form waves and cylindrically symmetric waves in higher dimensions have been recently studied. Our aim in this paper is to construct truly three-dimensional traveling waves. For a pyramid that satisfies a condition, we construct a traveling front for which the contour line has a pyramidal shape. We also construct generalized pyramidal fronts and traveling waves of a hybrid type between pyramidal waves and planar V-form waves. We use the comparison principles and construct traveling fronts between supersolutions and subsolutions.

    DOI: 10.1137/060661788

    Web of Science

    CiNii Article

    researchmap

  • Convergence to V-shaped fronts in curvature flows for spatially non-decaying initial perturbations

    M Nara, M Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   16 ( 1 )   137 - 156   2006.9

     More details

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

    This paper is concerned with the long time behavior for evolution of a curve governed by a curvature flow with constant driving force in the two-dimensional space. This problem has two types of traveling waves: traveling lines and V-shaped fronts, except for stationary circles. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. In this paper, we consider the uniform convergence of curves to the V-shaped fronts. Convergence results for a class of spatially non-decaying initial perturbations are established. Our results hold true with no assumptions on the smallness of given perturbations.

    Web of Science

    researchmap

  • Global stability of traveling curved fronts in the Allen-Cahn equations

    H Ninomiya, M Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   15 ( 3 )   819 - 832   2006.7

     More details

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

    This paper is concerned with the global stability of a traveling curved front in the Allen-Cahn equation. The existence of such a front is recently proved by constructing supersolutions and subsolutions. In this paper, we introduce a method to construct new subsolutions and prove the asymptotic stability of traveling curved fronts globally in space.

    Web of Science

    researchmap

  • Stability of a traveling wave in curvature flows for spatially non-decaying initial perturbations

    M Nara, M Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   14 ( 1 )   203 - 220   2006.1

     More details

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

    This paper is concerned with the long time behavior for the evolution of a curve governed by the curvature flow with constant driving force in two-dimensional space. Especially, the asymptotic stability of a traveling wave whose shape is a line is studied. We deal with moving curves represented by the entire graphs on the x-axis. By studying the Cauchy problem, the asymptotic stability of traveling waves with spatially decaying initial perturbations and the convergence rate are obtained. Moreover we establish the stability result where initial perturbations do not decay to zero but oscillate at infinity. In this case, we prove that one of the sufficient conditions for asymptotic stability is that a given perturbation is asymptotic to an almost periodic function in the sense of Bohr at infinity. Our results hold true with no assumptions on the smallness of given perturbations, and include the curve shortening flow problem as a special case.

    DOI: 10.3934/dcds.2006.14.203

    Web of Science

    researchmap

  • Existence and global stability of traveling curved fronts in the Allen-Cahn equations

    H Ninomiya, M Taniguchi

    JOURNAL OF DIFFERENTIAL EQUATIONS   213 ( 1 )   204 - 233   2005.6

     More details

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

    This paper is concerned with existence and stability of traveling curved fronts for the Allen-Cahn equation in the two-dimensional space. By using the supersolution and the subsolution, we construct a traveling curved front, and show that it is the unique traveling wave solution between them. Our supersolution can be taken arbitrarily large, which implies some global asymptotic stability for the traveling curved front. (c) 2004 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jde.2004.06.011

    Web of Science

    researchmap

  • Instability of planar traveling waves in bistable reaction-diffusion systems

    M Taniguchi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   3 ( 1 )   21 - 44   2003.2

     More details

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

    This paper is concerned with the stability of a planar traveling wave in a cylindrical domain. The equation describes activator-inhibitor systems in chemistry or biology. The wave has a thin transition layer and is constructed by singular perturbation methods. Let epsilon be the width of the layer. We show that, if the cross section of the domain is narrow enough, the traveling wave is asymptotically stable, while: it is unstable if the cross section is wide enough by studying the linearized eigenvalue problem.. For the latter case, we study the wavelength associated with an eigenvalue with the largest real part, which is called the fastest growing wavelength. We prove that this wavelength is O(epsilon(1/3)) as epsilon goes to zero mathematically rigorously. This fact shows that, if unstable planar waves are perturbed randomly, this fastest growing wavelength is selectively amplified with as time goes on. For this analysis, we use a new uniform convergence theorem for some inverse operator and carry out. the Lyapunov-Schmidt reduction.

    Web of Science

    researchmap

  • A uniform convergence theorem for singular limit eigenvalue problems

    Masaharu Taniguchi

    Advances in Differential Equations   8 ( 1 )   29 - 54   2003

     More details

  • Stability of traveling curved fronts in a curvature flow with driving force

    H. Ninomiya, M. Taniguchi

    Methods and Applications of Analysis   8 ( 3 )   429--450   2001

     More details

  • Multiple existence and linear stability of equilibrium balls in a nonlinear free boundary problem

    M Taniguchi

    QUARTERLY OF APPLIED MATHEMATICS   58 ( 2 )   283 - 302   2000.6

     More details

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

    This paper studies construction and linear stability of spherical interfaces in an equilibrium state in a two-phase boundary problem arising in activator-inhibitor models in chemistry. By studying the linearized eigenvalue problem near a given equilibrium ball, we show that the eigenvalues with nonnegative real parts are all real, and that they are characterized as values of a strictly convex function for specific discrete values of its argument. The stability is determined by the location of the zero points of this convex function. Using this fact, we present a criterion of stability in a useful form. We show examples and illustrate that stable equilibrium balls and unstable ones coexist near saddle-node bifurcation points in the bifurcation diagram, and a given equilibrium ball located far from bifurcation points is unstable and the eigenfunction associated with the largest eigenvalue consists of spherically harmonic functions of high degrees.

    Web of Science

    researchmap

  • Modified SLEP method by uniform convergence theorems for linearized eigenvalue problems

    M. Taniguchi

    Proceeding of International Conference on: Free Boundary Problems: Theory and Applications I, Gakkotosho   13   369 - 384   2000

     More details

  • Traveling curved fronts of a mean curvature flow with constant driving force

    H. Ninomiya, M. Taniguchi

    Proceeding of International Conference on: Free Boundary Problems: Theory and Applications I, Mathematical Sciences and Applications, Gakkotosho   13   206 - 221   2000

     More details

  • Instability of spherical interfaces in a nonlinear free boundary problem

    X. Chen, M. Taniguchi

    Advances in Differential Equations   5 ( 4-6 )   747 - 772   2000

     More details

  • Stability and characteristic wavelength of planar interfaces in the large diffusion limit of the inhibitor

    M Taniguchi, Y Nishiura

    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS   126   117 - 145   1996

     More details

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

    A characteristic wavelength and its parametric dependency are studied for planar interfaces of activator-inhibitor systems as well as their stability in two-dimensional space. When an unstable planar interface is slightly perturbed in a random way, it develops with a characteristic wavelength, that is, the fastest-growing one. A natural question is to ask under what conditions this characteristic wavelength remains finite and approaches a positive definite value as the width of interface, say epsilon, tends to zero. In this paper, we show that the fastest-growing wavelength has a positive limit value as epsilon tends to zero for the system:
    u(t) = Delta u + epsilon(-2) f(u, v), v(t) = epsilon(-1) Delta v + g(u, v).
    This is a fundamental fact for stuyding the domain size of patterns in higher-space dimensions.

    Web of Science

    researchmap

  • A remark on singular perturbation methods via the Lyapunov-Schmidt reduction

    M Taniguchi

    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES   31 ( 6 )   1001 - 1010   1995.12

     More details

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

    For some reaction-diffusion equations, Lyapunov-Schmidt reduction was shown to be applicable to construct singularly perturbed equilibrium solutions. For this application, it is indispensable to show that some inverse operator are uniformly bounded. In this paper, we give an elementary proof of this fact.

    DOI: 10.2977/prims/1195163593

    Web of Science

    researchmap

  • INSTABILITY OF PLANAR INTERFACES IN REACTION-DIFFUSION SYSTEMS

    M TANIGUCHI, Y NISHIURA

    SIAM JOURNAL ON MATHEMATICAL ANALYSIS   25 ( 1 )   99 - 134   1994.1

     More details

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

    Instability of planar front solutions to reaction-diffusion systems in two space dimensions is studied. Let epsilon denote the width of interface. Then the planar front solution-or a solution having an internal transition layer which is flat-loses its stability when the length of interface along the tangential direction exceeds O(epsilon(1/2)). The wavelength of the fastest growth is of O(epsilon(1/3)) which is inherent in the system and determined by the nonlinearity and diffusion coefficients. Complete asymptotic characterization of these quantities as a epsilon --> 0 is given by the analysis of what is called the singular dispersion relation derived from the linearized eigenvalue problem. The numerical computations also confirm that the theoretically predicted fastest growth wavy pattern actually arises from a randomly perturbed planar front.

    Web of Science

    researchmap

  • Bifurcation from flat-layered solutions to reaction diffusion systems in two space dimensions

    M. Taniguchi

    Journal of Mathematical Sciences The University of Tokyo   1 ( 2 )   339 - 367   1994

     More details

▼display all

Books

  • Traveling front solutions in reaction-diffusion equations

    谷口, 雅治

    Mathematical Society of Japan  2021  ( ISBN:9784864970976

     More details

    Total pages:xiii, 170 p.   Language:English

    CiNii Books

    researchmap

  • 特異摂動論(XI-9-2)

    丸善株式会社  2010 

     More details

  • 数学の言葉と論理

    朝倉書店  2008  ( ISBN:9784254117516

     More details

  • Allen-Cahn方程式における角錐型進行波

    2008 

     More details

Presentations

  • 等エネルギー型反応拡散方程式における軸非対称進行波 Invited

    谷口 雅治

    日本数学会函数方程式論分科会「微分方程式の総合的研究」  2019.12.22 

     More details

    Event date: 2019.12.21 - 2019.12.22

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

    researchmap

  • Allen-Cahn方程式における角錐型進行波 Invited

    谷口雅治

    非線形現象の数値シミュレーションと解析2008  2008.3.6 

     More details

    Event date: 2008.3.6 - 2008.3.7

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

    researchmap

  • Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations

    Masaharu Taniguchi

    2019.9.18 

     More details

    Language:Japanese   Presentation type:Oral presentation (general)  

    researchmap

  • Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations Invited

    Masaharu Taniguchi

    2019.9.10 

     More details

    Language:Japanese   Presentation type:Oral presentation (general)  

    researchmap

  • Axially asymmetric traveling fronts in balanced bistable reaction-diffusion equations Invited International conference

    Masaharu Taniguchi

    Recent Trends on Nonlinear PDEs of Elliptic and Parabolic Type, MATRIX Research Centre, Melbourne, Australia  2018.11.12 

     More details

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

    researchmap

  • Axially non-symmetric traveling fronts in balanced bistable reaction-diffusion equations

    Masaharu Taniguchi

    2018.9.25 

     More details

    Language:Japanese   Presentation type:Oral presentation (general)  

    researchmap

  • Pyramidal traveling fronts in the Allen-Cahn equations

    PDE Seminar, School of Mathematics  2008 

     More details

  • Allen-Cahn方程式における角錐型進行波の一意性と安定性

    日本数学会2008年度秋期総合分科会  2008 

     More details

  • Allen-Cahn方程式における角錐型進行波とその応用

    関数方程式セミナー  2008 

     More details

  • Pyramidal traveling fronts in the Allen-Cahn equations

    PDE Seminar, School of Mathematics  2008 

     More details

  • Stability of pyramidal traveling fronts in the Allen-Cahn equation

    Workshop on Singularities Arising in Nonlinear Problems 2007  2007 

     More details

  • Stability of pyramidal traveling fronts in the Allen-Cahn equation

    Workshop on Singularities Arising in Nonlinear Problems 2007  2007 

     More details

  • Allen-Cahn 方程式における多次元進行波

    日本数学会年会  2006 

     More details

▼display all

Research Projects

  • Mathematical analysis of pattern dynamics of reaction-diffusion systems and their singular limit problems

    Grant number:20H01816  2020.04 - 2024.03

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

    二宮 広和, 飯田 雅人, 谷口 雅治, 三竹 大寿, 物部 治徳

      More details

    Grant amount:\17420000 ( Direct expense: \13400000 、 Indirect expense:\4020000 )

    researchmap

  • Traveling fronts whose cross sections are convex shapes with major axes and minor axes in balanced bistable reaction-diffusion equations

    Grant number:20K03702  2020.04 - 2024.03

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

    谷口 雅治, 二宮 広和

      More details

    Grant amount:\4420000 ( Direct expense: \3400000 、 Indirect expense:\1020000 )

    researchmap

  • An (N-2)-dimensional surface with positive principal curvatures gives an N-dimensional traveling front in bistable reaction-diffusion equations

    Grant number:26400169  2014.04 - 2019.03

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

    Masaharu Taniguchi

      More details

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

    In this project, I consider a parabolic equation with a bistable nonlinear term. This equation is called the Allen--Cahn equation or the Nagumo equation.The aim of this project is to search unknown traveling fronts. The result is as follows. For every given compact convex set in the (N-1)-Euclidean space, I proved the existence
    of an N-dimensional traveling front solution associated with this set. Moreover, I proved that this traveling front solution is asymtotically stable if the given perturbation decays at infinity. These results were published by SIAM J. Math. Anal. 2015 and by J. Differential Equations 2016.

    researchmap

  • Pattern dynamics of reaction-diffusion systems and free boundary problems

    Grant number:26287024  2014.04 - 2018.03

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

    Ninomiya Hirokazu, MONOBE Harunori

      More details

    Grant amount:\16510000 ( Direct expense: \12700000 、 Indirect expense:\3810000 )

    To study the spatial patterns of solutions of partial differential equations, such as reaction-diffusion systems, we introduce a reaction-interface system, which consists of the interface equation and an equation in the whole space. This is derived as a singular limit of some reaction-diffusion systems. We studied the multidimensional traveling wave solution and the pulse dynamics of the reaction-interface system. Moreover, for the curvature flow with the anisotropic external force, we study the influence of the anisotropy to the compact traveling wave solutions. We also introduce the layered system to analyze the spatial profiles of solutions in multidimensional space.

    researchmap

  • Three-dimensional cylindrically non-symmetric traveling fronts in reaction-diffusion equations

    Grant number:23540235  2011 - 2013

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

    TANIGUCHI Masaharu

      More details

    Grant amount:\5070000 ( Direct expense: \3900000 、 Indirect expense:\1170000 )

    The results are as follows. (1) We proved N-dimensional pyramidal traveling fronts in the Allen-Cahn (Nagumo) equation.(2) We consider the Allen-Cahn (Nagumo) equation in the three-dimensional space, and proved the existence and stability of cylindrically non-symmetric traveling fronts. The cross sections of these traveling fronts are smooth convex shapes, say, ellipses. (3) We prove the existence of N-dimensional pyramidal traveling fronts in competition-diffusion systems. (4) We prove the non-existence of localized traveling spots with non-zero speed in a single reaction-diffusion equation under some condition.

    researchmap

  • Global stability of multi-dimensional traveling fronts

    Grant number:18540208  2006 - 2009

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

    TANIGUCHI Masaharu

      More details

    Grant amount:\4150000 ( Direct expense: \3400000 、 Indirect expense:\750000 )

    I studied the Allen-Cahn equation (Nagumo equation) in three-dimensional Euclidean space, and constructed pyramidal traveling front solutions and convex polyhedral traveling front solutions. I also proved that they are stable for given fluctuations.

    researchmap

▼display all

 

Class subject in charge

  • Advanced practice in scientific presentation (2021academic year) special  - その他

  • Partial Differential Equations (2021academic year) Prophase  - 火1,火2

  • Internship for advanced research (2021academic year) special  - その他

  • Advanced Experiment (2021academic year) special  - その他

  • Practice in Scientific Presentation 1 (2021academic year) Concentration  - その他

  • Practice in Scientific Presentation 2 (2021academic year) Late  - その他

  • Global seminar in interdisciplinary science (2021academic year) special  - その他

  • Introduction to Interdisciplinary Science 1 (2021academic year) Prophase  - 水1,水2

  • Introduction to Interdisciplinary Science 2 (2021academic year) Prophase  - 水1,水2

  • Calculus III (2021academic year) 1st and 2nd semester  - 月3,月4

  • Calculus IIIa (2021academic year) 1st semester  - 月3,月4

  • Exercises in Calculus IIIa (2021academic year) 1st semester  - 月5,月6

  • Calculus IIIb (2021academic year) Second semester  - 月3,月4

  • Exercises in Calculus IIIb (2021academic year) Second semester  - 月5,月6

  • Exercises in Calculus III (2021academic year) 1st and 2nd semester  - 月5,月6

  • Group Study on Mathematical Sciences (2021academic year) special  - その他

  • Group Study on Mathematical Sciences (2021academic year) special  - その他

  • Seminar in Mathematical Analysis (2021academic year) Year-round  - その他

  • Philosophy and ethics in the science (2021academic year) special  - その他

  • Advanced Analysis II (2021academic year) 3rd and 4th semester  - 月7,月8

  • Advanced Analysis IIa (2021academic year) Third semester  - 月7,月8

  • Advanced Analysis IIb (2021academic year) Fourth semester  - 月7,月8

  • Seminar in Mathematics (2021academic year) special  - その他

  • Seminar in Mathematics (2021academic year) special  - その他

  • Mathematical Theory on Traveling Waves (2021academic year) Late  - その他

  • Discrete Mathematics II (2021academic year) 3rd and 4th semester  - 月5,月6

  • Discrete Mathematics IIa (2021academic year) Third semester  - 月5,月6

  • Discrete Mathematics IIb (2021academic year) Fourth semester  - 月5,月6

  • Advanced practice in scientific presentation (2020academic year) Year-round  - その他

  • Partial Differential Equations (2020academic year) Prophase  - 火1,火2

  • Internship for advanced research (2020academic year) Year-round  - その他

  • Advanced Experiment (2020academic year) special  - その他

  • Practice in Scientific Presentation 1 (2020academic year) Summer concentration  - その他

  • Practice in Scientific Presentation 2 (2020academic year) Late  - その他

  • Global seminar in interdisciplinary science (2020academic year) Year-round  - その他

  • Introduction to Interdisciplinary Science 1 (2020academic year) Prophase  - 水1,水2

  • Introduction to Interdisciplinary Science 2 (2020academic year) Prophase  - 水1,水2

  • Calculus III (2020academic year) 1st and 2nd semester  - 月3,月4

  • Calculus IIIa (2020academic year) 1st semester  - 月3,月4

  • Exercises in Calculus IIIa (2020academic year) 1st semester  - 月5,月6

  • Calculus IIIb (2020academic year) Second semester  - 月3,月4

  • Exercises in Calculus IIIb (2020academic year) Second semester  - 月5,月6

  • Exercises in Calculus III (2020academic year) 1st and 2nd semester  - 月5,月6

  • Advanced lectures in Mathematics (2020academic year) Summer concentration  - その他

  • Seminars in Mathematics and Physics (2020academic year) Other  - その他

  • Seminars in Mathematics and Physics (2020academic year) Year-round  - その他

  • Advanced Study in Mathematics and Physics (2020academic year) Other  - その他

  • Advanced Study in Mathematics and Physics (2020academic year) Year-round  - その他

  • Glance at Mathematical Science C (2020academic year) Third semester  - 金5,金6

  • Group Study on Mathematical Sciences (2020academic year) special  - その他

  • Group Study on Mathematical Sciences (2020academic year) special  - その他

  • Seminar in Mathematical Analysis (2020academic year) Prophase

  • Seminar in Mathematical Analysis (2020academic year) Other  - その他

  • Seminar in Mathematical Analysis (2020academic year) Year-round  - その他

  • Philosophy and ethics in the science (2020academic year) Year-round  - その他

  • Advanced Analysis II (2020academic year) 3rd and 4th semester  - 月7,月8

  • Advanced Analysis IIa (2020academic year) Third semester  - 月7,月8

  • Advanced Analysis IIb (2020academic year) Fourth semester  - 月7,月8

  • Seminar in Mathematics (2020academic year) special  - その他

  • Seminar in Mathematics (2020academic year) special  - その他

  • Seminar in Mathematics (2020academic year) 1st and 2nd semester  - その他

  • Mathematical Theory on Traveling Waves (2020academic year) Prophase  - その他

▼display all

 

Social Activities

  • 教員免許状更新講習会

    Role(s):Lecturer

    岡山大学  2020.8.19

     More details

    Type:Certification seminar

    researchmap