Organization
Organization Organization for the Strategic Coordination of Research and Intellectual Properties Professor (non-tenured)
Title
Professor (non-tenured)
External link
Degree
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Doctor of Mathematical Sciences ( The University of Tokyo )
Research Interests
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Infinite dimensional dynamical systems
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Nonlinear partial differential equations
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Reaction-diffusion systems
Research Areas
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Natural sciences / Basic mathematics
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Natural sciences / Applied mathematics and statistics
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Natural sciences / Mathematical analysis
Education
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The University of Tokyo Graduate School of Mathematical Sciences Department of Mathematical Sciences
1993.4 - 1997.3
Country/Region： Japan
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The University of Tokyo Graduate School of Mathematical Sciences Department of Mathematical Sciences
1991.4 - 1993.3
Country/Region： Japan
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The University of Tokyo Faculty of Science Department of Mathematics
1987.4 - 1991.3
Country/Region： Japan
Research History
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Meiji University
2023.4
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金沢大学 准教授
2011.4 - 2023.3
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電気通信大学 助教
2007.4 - 2011.3
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電気通信大学 助手
1997.4 - 2007.3
Professional Memberships
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日本応用数理学会
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日本数理生物学会
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日本数学会
Committee Memberships
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日本数学会 応用数学分科会 評議員
2022.3 - 2024.2
Committee type：Academic society
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日本数学会 応用数学分科会委員
2009.10 - 2011.9
Committee type：Academic society
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日本数学会 学会誌編集委員
2006 - 2008
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日本応用数理学会 学会誌編集委員
2003.4 - 2006.4
Papers
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Asymmetric front propagation for the bistable reaction-diffusion equation on a metric graph Reviewed
Toru Kan, Yoshihisa Morita, Ken-Ichi Nakamura, Chang-Hong Wu
Journal of Differential Equations 457 114039 - 114039 2026.3
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Front propagation and blocking for the competition-diffusion system in a domain of half-lines with a junction Invited Reviewed
Yoshihisa Morita, Ken-Ichi Nakamura, Toshiko Ogiwara
Discrete and Continuous Dynamical Systems - B 28 ( 12 ) 6345 - 6361 2023.12
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On the reaction–diffusion type modelling of the self-propelled object motion Reviewed
Masaharu Nagayama, Harunori Monobe, Koya Sakakibara, Ken-Ichi Nakamura, Yasuaki Kobayashi, Hiroyuki Kitahata
Scientific Reports 13 ( 1 ) 2023.8
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Traveling wave dynamics for Allen-Cahn equations with strong irreversibility Reviewed
Goro Akagi, Christian Kuehn, Ken-Ichi Nakamura
Transactions of the American Mathematical Society 375 3173 - 3238 2022.2
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Stability of stationary points for one-dimensional Willmore energy with spatially heterogeneous term Reviewed
Masaaki Uesaka, Ken-Ichi Nakamura, Keiichi Ueda, Masaharu Nagayama
Physica D: Nonlinear Phenomena 417 132812 - 132812 2021.3
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Traveling wave solutions for a predator–prey system with two predators and one prey Reviewed
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chin-Chin Wu
Nonlinear Analysis: Real World Applications 54 103111 - 103111 2020.8
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The sign of traveling wave speed in bistable dynamics Reviewed
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chang-Hong Wu
Discrete & Continuous Dynamical Systems - A 40 ( 6 ) 3451 - 3466 2020.6
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Stability and uniqueness of traveling waves for a discrete bistable 3-species competition system Reviewed
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chin-Chin Wu
Journal of Mathematical Analysis and Applications 472 ( 2 ) 1534 - 1550 2019.4
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Numerical approach to three-dimensional model of cellular electrophysiology by the method of fundamental solutions Invited Reviewed
Ken-Ichi Nakamura, Koya Sakakibara, Shigetoshi Yazaki
JSIAM Letters 11 17 - 20 2019.3
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Recurrent traveling waves in a two-dimensional saw-toothed cylinder and their average speed Reviewed
Bendong Lou, Hiroshi Matano, Ken-Ichi Nakamura
Journal of Differential Equations 255 ( 10 ) 3357 - 3411 2013.11
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A stable finite difference method for a Cahn-Hilliard type equation with long-range interaction Reviewed
Hikaru Matsuoka, Ken-Ichi Nakamura
Science Reports of Kanazawa University 57 13 - 34 2013
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PERIODICALLY GROWING SOLUTIONS IN A CLASS OF STRONGLY MONOTONE SEMIFLOWS Invited Reviewed
Ken-Ichi Nakamura, Toshiko Ogiwara
NETWORKS AND HETEROGENEOUS MEDIA 7 ( 4 ) 881 - 891 2012.12
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Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit Reviewed
Hiroshi Matano, Ken-Ichi Nakamura, Bendong Lou
NETWORKS AND HETEROGENEOUS MEDIA 1 ( 4 ) 537 - 568 2006.12
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On the steadily rotating spirals Reviewed
JS Guo, KI Nakamura, T Ogiwara, JC Tsai
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 23 ( 1 ) 1 - 19 2006.2
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Bifurcations of steady states for the Eguchi-Oki-Matsumura model of phase separation Reviewed
Naoyuki Ishimura, Ken-Ichi Nakamura, Masaaki Nakamura
Applicable Analysis 85 ( 6-7 ) 831 - 843 2006
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Blow-up solutions appearing in the vorticity dynamics with linear strain Reviewed
K. I. Nakamura, H. Okamoto, H. Yagisita
Journal of Mathematical Fluid Mechanics 6 ( 2 ) 157 - 168 2004.6
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Spiral traveling wave solutions of nonlinear diffusion equations related to a model of spiral crystal growth Reviewed
T Ogiwara, KI Nakamura
PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES 39 ( 4 ) 767 - 783 2003.12
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Asymptotic behavior of solutions for nonlinear diffusion equations Reviewed
Toshiko Ogiwara, ken-Ichi Nakamura
Proceedings of the second international conference on non-linear analysis and convex analysis 363 - 372 2003
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Spiral traveling wave solutions of some parabolic equations on annuli Reviewed
Toshiko Ogiwara, Ken-Ichi Nakamura
Josai Mathematical Monographs 2 15 - 34 2000
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Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term Reviewed
KI Nakamura, H Matano, D Hilhorst, R Schatzle
JOURNAL OF STATISTICAL PHYSICS 95 ( 5-6 ) 1165 - 1185 1999.6
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The global attractor of semilinear parabolic equations on S^1 Reviewed
Hiroshi Matano, Ken-Ichi Nakamura
Discrete and Continuous Dynamical Systems 3 ( 1 ) 1 - 24 1997
MISC
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Homogenization limit of recurrent traveling waves in a two-dimensional cylinder with undulating boundary
International Associated Laboratory "Reaction-Diffusion Laboratory" 2010
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Homogenization limit of recurrent traveling waves in a two-dimensional cylinder with undulating boundary
International Associated Laboratory "Reaction-Diffusion Laboratory" 2010
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Existence of recurrent traveling waves in a 2D saw-toothed cylinder --- the virtual pinning case
University of Paris-Sud 2010
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Existence of recurrent traveling waves in a 2D saw-toothed cylinder --- the virtual pinning case
University of Paris-Sud 2010
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多安定型反応拡散方程式におけるフロントの相互作用
日本数学会 164 - 167 2009
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Homogenization limit of recurrent traveling waves in a saw-toothed cylinder
International Associated Laboratory "Reaction-Diffusion Laboratory" 2009
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Homogenization limit of recurrent traveling waves in a saw-toothed cylinder
International Associated Laboratory "Reaction-Diffusion Laboratory" 2009
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Traveling waves in a two-dimensional saw-toothed cylinder and their homogenization limit
International Associated Laboratory "Reaction-Diffusion Laboratory" 2008
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Asymptotic stability of traveling waves in heterogeneous media
International Associated Laboratory "Reaction-Diffusion Laboratory" 2008
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均質化の基本的なアイデアと不均質媒体中のフロント伝播への応用
1597 62 - 68 2008
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Asymptotic stability of traveling waves in heterogeneous media
International Associated Laboratory "Reaction-Diffusion Laboratory" 2008
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非一様な場を伝播する進行波の速度
日本数学会 2008
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Traveling waves in a two-dimensional saw-toothed cylinder and their homogenization limit
International Associated Laboratory "Reaction-Diffusion Laboratory" 2008
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Front propagation in heterogeneous media
盛岡応用数学小研究集会報告集 55 - 67 2007
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Front propagation in heterogeneous media
55 - 67 2007
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Traveling waves in a 2-dimensional cylinder with undulating boundary
数理解析研究所 2006
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Large time behavior of unbounded global solutions to some nonlinear diffusion equations
RIMS 73--81 2006
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Asymptotic study of front propagation in heterogeneous environments
International Associated Laboratory "Reaction-Diffusion Laboratory" 2006
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Traveling waves in a 2-dimensional cylinder with undulating boundary
2006
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Traveling waves in a 2-dimensional cylinder with saw-toothed boundary
2006
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Speed of front propagation for a competition-diffusion system with variable coefficients
American Institute of Mathematical Sciences 2006
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Speed of propagation of traveling fronts in periodic media governed by a bistable nonlinearity
BIRS 2006
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Speed of front propagation for a competition-diffusion system with variable coefficients
American Institute of Mathematical Sciences 2006
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Speed of propagation of traveling fronts in periodic media governed by a bistable nonlinearity
BIRS 2006
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NAKAMURA KEN-ICHI, OGIWARA TOSHIKO
RIMS Kokyuroku 1464 73--81 - 172 2006
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Asymptotic study of front propagation in heterogeneous environments
International Associated Laboratory "Reaction-Diffusion Laboratory" 2006
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Traveling waves in a 2-dimensional cylinder with saw-toothed boundary
慶應義塾大学 2006
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Periodic traveling waves in an undulating band domain
University of Paris-Sud 2005
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Large time behavior of unbounded global solutions to some nonlinear diffusion equations
RIMS 2005
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Effective speed of propagating fronts in spatially inhomogeneous media
CIRM 2005
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Large time behavior of unbounded global solutions to some nonlinear diffusion equations
RIMS 2005
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Effective speed of propagating fronts in spatially inhomogeneous media
CIRM 2005
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Periodic traveling waves in an undulating band domain
University of Paris-Sud 2005
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Steadily rotating spirals in the kinematic theory of excitable media
日本数学会 ??-?? 2005
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Effective speed of propagating fronts in periodic media
Nihon University 2004
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Bounds for effective speeds of traveling fronts in spatially periodic media
University of Paris-Sud 2004
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Propagation speeds of traveling fronts in spatially periodic media
National Taiwan Normal University 2004
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Effective speed of propagating fronts in periodic media
Nihon University 2004
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Traveling waves in a band domain with quasi-periodically undulating boundaries
RIMS 73 - 81 2004
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Bounds for effective speeds of traveling fronts in spatially periodic media
University of Paris-Sud 2004
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Lou Bendong, Matano Hiroshi, Nakamura Ken-Ichi
RIMS Kokyuroku 1356 73 - 81 2004
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Propagation speeds of traveling fronts in spatially periodic media
National Taiwan Normal University 2004
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Asymptotic behavior of solutions to a quasi-linear parabolic equation
71 - 76 2003
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Asymptotic behavior of solutions to a quasi-linear parabolic equation
71 - 76 2003
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Nakamura Ken-Ichi
RIMS Kokyuroku 1330 79--87 - 87 2003
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Bounds for effective speeds of traveling fronts in spatially periodic media
79--87 2003
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Propagation speeds of traveling fronts in periodic media governed by a bistable nonlinearity
2003
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古典的曲率流の自己相似解の分類 -- Abresch-Langerの方法の再考 --
「巨大領域のための有限要素法と領域分割計算ならびに関連事項」横浜研究会講演概要集 26--35 2003
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Bounds for the propagation speeds of traveling fronts in heterogeneous media
日本数学会 97 - 100 2003
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曲率流方程式の自己相似解の分類 -- Abresch-Langerの方法の再考 --
日本数学会 93 - 96 2003
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岡本 久, 中村 健一, 柳下 浩紀
数理解析研究所講究録 1322 102 - 106 2003
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Propagation speeds of traveling fronts in periodic media governed by a bistable nonlinearity
北海道大学電子科学研究所 2003
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Asymptotic behavior of solutions to a model of spiral crystal growth
72 - 84 2002
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Bounds for effective speeds of traveling fronts in spatially periodic media
RIMS 2002
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Effective speed of pulsating traveling fronts in periodic media
University of L'Aquila 2002
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Ogiwara Toshiko, Nakamura Ken-ichi
RIMS Kokyuroku 1258 72 - 84 2002
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Effective speed of pulsating traveling fronts in periodic media
University of L'Aquila 2002
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古典的曲率流の自己相似解の分類 -- Abresch-Langerの方法の再考 --
応用数学合同研究集会報告集 199 - 202 2002
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Bounds for effective speeds of traveling fronts in spatially periodic media
RIMS 2002
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Effective speed of traveling front solutions of bistable reaction-diffusion equations
2001
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Spiral wave solutions to a model of crystal growth
Kobe Institute 2001
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Asymptotic behavior of solutions for nonlinear diffusion equations
Abstracts of the second international conference on nonlinear analysis and convex analysis 58 2001
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Asymptotic behavior of solutions for nonlinear diffusion equations
58 2001
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Asymptotic behavior of solutions for nonlinear diffusion equations
Abstracts of the second international conference on nonlinear analysis and convex analysis 58 2001
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Asymptotic behavior of solutions to a model of spiral crystal growth
ISAAC 2001
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Effective speeds of traveling fronts in almost periodic media
応用数学合同研究集会報告集 167 - 170 2001
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Asymptotic behavior of solutions for nonlinear diffusion equations
58 2001
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Spiral wave solutions to a model of crystal growth
Kobe Institute 2001
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Asymptotic behavior of solutions to a model of spiral crystal growth
ISAAC 2001
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Effective speed of traveling front solutions of bistable reaction-diffusion equations
2001
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Effective speed of traveling wavefronts in periodic inhomogeneous media
2000
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Spiral traveling wave solutions for nonlinear diffusion equations
国際高等研究所 2000
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Spiral traveling wave solutions for some nonlinear diffusion equations
35 - 39 2000
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準完全結晶の成長モデルに現れるらせん状解の漸近挙動
2000年応用数学合同研究集会報告集，龍谷大学 191 - 194 2000
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ある反応拡散方程式に現れる多重らせん進行波解について
日本数学会 93 - 95 2000
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Effective speed of traveling wavefronts in periodic inhomogeneous media
2000
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Spiral traveling wave solutions for some nonlinear diffusion equations
35 - 39 2000
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Spiral traveling wave solutions of some parabolic equations on annuli
Ogiwara Toshiko, Nakamura Ken-ichi
Mathematical bulletin of the Graduate School of Science, Josai University 3 99 - 118 2000
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Spiral traveling wave solutions for nonlinear diffusion equations
国際高等研究所 2000
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Singular limit of a reaction-diffusion equation with a spatially inhomogeneous reaction term
KI Nakamura, H Matano, D Hilhorst, R Schatzle
JOURNAL OF STATISTICAL PHYSICS 95 ( 5-6 ) 1165 - 1185 1999.6
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Effective speed of travelling wavefronts in inhomogeneous media
53 - 60 1999
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Effective speed of travelling wavefronts in inhomogeneous media
53 - 60 1999
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ある反応拡散方程式に現れるらせん状進行波解について
応用数学合同研究集会報告集，龍谷大学 279 - 282 1999
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周期的非一様性をもつ拡散方程式の進行波
第47回応用力学連合会講演会予稿集 1998
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Travelling waves for a diffusion equation with periodic inhomogeneity
Colloquium Lectures, Hokkaido Univ. Technical Report Series in Mathematics 55 21 - 24 1998
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Travelling waves for a diffusion equation with periodic inhomogeneity
Colloquium Lectures, Hokkaido Univ. Technical Report Series in Mathematics 55 21 - 24 1998
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Travelling waves for a diffusion equation with periodic inhomogeneity
Colloquium Lectures, Hokkaido Univ. Technical Report Series in Mathematics 1998
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Travelling waves for a diffusion equation with periodic inhomogeneity
Colloquium Lectures, Hokkaido Univ. Technical Report Series in Mathematics 1998
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空間的に非一様な反応拡散方程式に現れる界面の挙動について
第4回阿波ワークショップ'97講演論文集 13 - 18 1998
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Pseudo-travelling waves for a diffusion equation with periodic inhomogeneity
「パターンの数理的研究とその周辺」予稿集 7 - 12 1998
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Effective speed of travelling wavefronts in inhomogeneous media
Ryukoku University 1998
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Effective speed of travelling wavefronts in inhomogeneous media
Ryukoku University 1998
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Travelling waves for a diffusion equation with periodic inhomogeneity
日本数学会 131 - 134 1997
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The Global Attractor of Semilinear Parabolic Equations on S<sup>1</sup>(共著)
Discrete and Continuous Dynamical Systems 3 ( 1 ) 1 - 24 1997
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周期的空間構造をもつ媒体上の擬似進行波
研究集会「自由境界問題に対する数学解析・数値解析」報告集 15--22 1997
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周期的空間構造をもつ媒体上の擬似進行波
15--22 1997
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半線形放物型方程式の周期解分岐の大域的構造
阿波ワークショップ'95「第3回先端技術における数理モデル解析」講演論文集 101--109 1996
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Bifurcation and orbital connections of rotating waves in a semilinear heat equation on S^1
研究集会「非線形問題の解析」報告集 33--42 1996
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Bifurcation and orbital connections of rotating waves in a semilinear heat equation on S^1
研究集会「非線形問題の解析」報告集 33--42 1996
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半線形放物型方程式における周期解どうしのコネクションの存在
日本数学会 62--63 1995
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S^1上の半線形放物型方程式における周期解の分岐の大域的構造
日本数学会 60--61 1995
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S^1上の半線形拡散方程式の周期解の分岐構造
応用数学合同研究集会報告集 49-1--49-6 1995
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S^1上の半線形放物型方程式の大域アトラクターについて
日本数学会 41 1994
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空間1次元半線形放物型方程式の大域アトラクターについて
日本数学会 166--169 1993
Presentations
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Speed of bistable traveling wave in a three-species competitive Lotka-Volterra model with diffusion Invited
Ken-Ichi Nakamura
2025 Japan-Taiwan Joint Workshop: Reaction-Diffusion Models and Partial Differential Equations 2025.3
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Bistable traveling waves in 3-species cooperation/competition models with diffusion Invited
中村 健一
非線形現象の数値シミュレーションと解析 2025 2025.3
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The speed of bistable traveling fronts in the Lotka-Volterra competition-diffusion system Invited
Ken-Ichi Nakamura
The 14th AIMS Conference on Dynamical Systems, Differential Equations and Applications 2024.12
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The sign of the speed of bistable traveling fronts in multi-species models Invited
Ken-Ichi Nakamura
ReaDiNet 2024: Recent Progresses in the theory of reaction and diffusion equations 2024.10
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The speed of bistable traveling fronts in the Lotka-Volterra competition-diffusion system Invited
Ken-Ichi Nakamura
A ReaDiNet workshop on reaction-diffusion systems and population dynamics 2024.6
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Sign-definiteness conditions for the speed of bistable traveling fronts of the Lotka-Volterra competition-diffusion system Invited
Ken-Ichi Nakamura
NCTS Workshop on Bifurcation Phenomena and Evolutionary Equations 2024.4
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The role of species mobility in competitive exclusion Invited
Ken-Ichi Nakamura
2024.3
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Front propagation for Lotka-Volterra competition-diffusion system on star-shaped noncompact graphs Invited
Ken-Ichi Nakamura
One-day workshop on PDEs and related topics 2024.2
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A remark on the speed of bistable traveling waves for the Lotka-Volterra competition-diffusion system Invited
Ken-Ichi Nakamura
Turing Symposium on Morphogenesis, 2024 — a Panorama in Turing's Sight — 2024.2
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Propagation direction of traveling fronts in competition-diffusion system with symmetric nonlinearity Invited
2024.2
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Front propagation for Lotka-Volterra competition-diffusion system on unbounded star graphs Invited
Ken-Ichi Nakamura
ICIAM2023 2023.8
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The speed of bistable traveling waves for the Lotka-Volterra competition-diffusion system on a one-dimensional lattice Invited
2023.6
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The sign of the speed of bistable traveling waves for the Lotka-Volterra competition-diffusion system Invited
Ken-Ichi Nakamura
13th AIMS International Conference on Dynamical Systems, Differential Equations and Applications 2023.5
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Front propagation and blocking for the Lotka-Volterra strong competition system in an infinite star graph Invited
Ken-Ichi Nakamura
International Conference on Applied Mathematics 2023.5
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Front propagation and blocking for the Lotka-Volterra strong competition in an infinite star graph Invited
Ken-Ichi Nakamura
ReaDiNet2023: International Conference on Parabolic and Stochastic Models in Mathematical Biology 2023.1
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Propagation speed of bistable traveling waves for the Lotka-Volterra competition-diffusion model Invited
中村 健一
非線形現象の数値シミュレーションと解析2022 2022.3
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Lotka-Volterra diffusion system with strong competition: the propagation direction of traveling waves Invited
中村 健一
第5回反応拡散方程式と非線形分散方程式の解の挙動 2022.2
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基底膜変形モデルの数理解析 Invited
中村 健一
第16回 生物数学の理論とその応用 2020.1
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Lotka-Volterra２種競争拡散系の双安定進行波の伝播方向 Invited
中村 健一
芝浦工大数理科学科談話会 2024.10
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Lotka-Volterra 競争拡散系の双安定進行波の伝播方向 Invited
中村 健一
金沢解析セミナー 2023.3
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強競争ロトカ・ヴォルテラ拡散系の進行波の伝播方向 Invited
中村 健一
日本数理生物学会2022年度年会 数理生物に関連する反応拡散系の最近の話題 2022.9
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表皮基底膜の変形に関連するエネルギー最小化問題 Invited
中村 健一
CREST「現代の数理科学と連携するモデリング手法の構築」成果報告公開シンポジウム 2021.9
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進行波の速度によるLotka-Volterra 2種競争系の強競争条件の分類
中村 健一
日本数学会2021年度秋季総合分科会 函数方程式論分科会 2021.9
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Front propagation and blocking of the competition-diffusion system in a domain of half-lines with a junction
2021.9
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星状グラフの分岐点における2種競争拡散系のフロント解の通過・停止
中村 健一
日本応用数理学会2021年度年会 現象の数理モデリングと数理解析 2021.9
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Speed of traveling waves for discrete bistable Lotka–Volterra competition system
2020.9
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Existence and stability of symmetric solutions of a variational problem for plane curves Invited
2019.10
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Existence and stability of symmetric solutions of a variational problem for plane curves Invited
Ken-Ichi Nakamura
2019.9
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Global asymptotic stability of traveling fronts for a bistable 3-component lattice dynamical system Invited International conference
Ken-Ichi Nakamura
Mini-workshop on Nonlinear Diffusion Problems 2019.6 Research Center of Mathematics for Social Creativity, RIES, Hokkaido University
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Monotone Traveling Waves for a Bistable Lattice Dynamical System Invited International conference
Ken-Ichi Nakamura
SIAM Conference on Applications of Dynamical Systems 2019.5 Society for Industrial and Applied Mathematics (SIAM)
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双安定型進行フロント波の単調性・安定性・速度 Invited
中村 健一
第二回はこだて現象数理研究集会 2019.5
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Uniqueness and stability of monotone traveling waves for bistable lattice dynamical systems Invited International conference
Ken-Ichi Nakamura
2018 China-Japan Workshop on Nonlinear Diffusion Problems 2018.11
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Asymptotic Stability of Traveling Waves for Bistable Lattice Dynamical Systems of Cooperation Type Invited International conference
Ken-Ichi Nakamura
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications 2018.7
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Effect of Diffusion Type on the Propagation Speed of Traveling Fronts in Periodic Environments Invited International conference
Ken-Ichi Nakamura
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications 2018.7
-
Asymptotic stability of monotone traveling waves for bistable lattice dynamical systems Invited International conference
Ken-Ichi Nakamura
International Conference on Nonlinear Analysis and its Applications 2018.3
Research Projects
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Study on the dynamics of propagation in population models with biological dispersal and its application to the problem of alien species invasion
Grant number：25K07124 2025.4 - 2029.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
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自己駆動体運動を記述する反応拡散系モデルとその数理解析
Grant number：25K00918 2025.4 - 2029.3
日本学術振興会 科学研究費助成事業 基盤研究(B)
長山 雅晴, 北畑 裕之, 榊原 航也, 中村 健一, 中田 聡, 高棹 圭介
Grant amount：\18850000 （ Direct Cost: \14500000 、 Indirect Cost：\4350000 ）
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比較定理を基軸に展開する生態系ネットワーク上の生物種の侵入・停留の数学解析
Grant number：22K03418 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)
中村 俊子, 中村 健一
Grant amount：\4030000 （ Direct Cost: \3100000 、 Indirect Cost：\930000 ）
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Quantitative analysis for nonlinear evolution equations of diffusion type
Grant number：21KK0044 2021.10 - 2027.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))
Grant amount：\18200000 （ Direct Cost: \14000000 、 Indirect Cost：\4200000 ）
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自己駆動体の集団運動に対する数理モデリングと数理解析
Grant number：21H00996 2021.4 - 2025.3
日本学術振興会 科学研究費助成事業 基盤研究(B)
長山 雅晴, 北畑 裕之, 中村 健一, 田中 晋平, 中田 聡, 後藤田 剛
Grant amount：\17290000 （ Direct Cost: \13300000 、 Indirect Cost：\3990000 ）
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自己駆動体の集団運動に対する数理モデリングと数理解析
Grant number：23K20808 2021.4 - 2025.3
日本学術振興会 科学研究費助成事業 基盤研究(B)
長山 雅晴, 北畑 裕之, 中村 健一, 田中 晋平, 中田 聡, 後藤田 剛
Grant amount：\17290000 （ Direct Cost: \13300000 、 Indirect Cost：\3990000 ）
水面の表面張力を変化させることで運動する自己駆動体が複数個あるときに観察される集団運動を理論的に解明することによって、集団運動の形成される要因が示され、生物が見せる集団運動原理の解明に繋がることが期待できる。この研究では、数理モデリングと実験検証の相補的研究によって、自己駆動体に現れる集団運動の発現機構およびその形成機構について数理科学的点からメカニズム解明を目指している。
2023年度は，2022年度に構築した自己駆動体運動を記述する体積保存型Phase-Fieldモデルに対して、L2勾配流モデルとして新しく体積保存型Phase-Field方程式の導出に成功した。この数理モデルは前年度構築した数理モデルと一部異なっているが，特異極限系は前年度構築した反応拡散系モデルと同一であることを明らかにした。これによって最終的にL2勾配流を基盤とした自己駆動体運動モデルを完成させた。このL2勾配流型体積保存Phase-Fieldモデルをさらに発展させ、三角形形状、四角形形状等の任意の正多角形形状や楕円形状、ダンベル形状の自己駆動体を表現するL2勾配流型体積保存Phase-Fieldモデルの構築を行った。反応拡散系モデルでは一般に変形と回転が区別できないが、我々の定式化によって回転運動と並進運動を起こす自己駆動体運動モデルを反応拡散系モデルで表現することに成功した。さらに、楕円形状自己駆動体は短軸方向への運動が安定であることが数値的に示され、これまでの数理モデルでの結果と矛盾しないことを明らかにした。この数理モデルを用いて排除体積効果を含めることによって、複数の自己駆動体運動を表現する数理モデルの構築に成功した。今後この数理モデルを用いて、自己駆動体の集団運動実験を再現し，集団運動形成メカニズムを理論的に示していく。 -
メタ群集モデルの数理解析・数値解析による生物種の侵入制御可能性の探究
Grant number：21K03368 2021.4 - 2024.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Authorship：Principal investigator
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
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個体群動態モデルに現れる界面ダイナミクスの数理解析・数値解析
2018.4 - 2021.3
日本学術振興会 科学研究費補助金 基盤研究(C)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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Mathematical modeling of collectiove motion of self-propelled systems and its analysis
Grant number：16H03949 2016.4 - 2020.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
NAGAYAMA MASAHARU
Grant amount：\17680000 （ Direct Cost: \13600000 、 Indirect Cost：\4080000 ）
We carried out mathematical modeling of the self-propelled system and performed mathematical analysis of the mathematical model. In this research, together with the experimental group, we solved the mechanism of oscillation phenomena about the self-propelled material by mathematical modeling. Moreover, it was clarified that the mechanism of collective motion that occurs when multiple self-propelled materials float on the water is not caused by the capillarity phenomenon but is caused by the concentration gradient of the chemical substances contained in the aqueous solution near the water surface. In addition, we have clarified the mechanism of the interaction motion between the string-shaped self-propelled materials and the shape-dependent interaction motion between the self-propelled materials by mathematical modeling and theoretical analysis.
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生体内の不均一な場における反応拡散波の伝播機構の解明
2015.7 - 2018.3
日本学術振興会 科学研究費補助金 基盤研究(C) 特設分野
中村 健一
Authorship：Principal investigator Grant type：Competitive
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結晶表面におけるステップダイナミクスの数理解析・数値解析
2015.4 - 2019.3
日本学術振興会 科学研究費補助金 基盤研究(C)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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Spot dynamics of the volume preserving reaction-diffusion systems
Grant number：25610029 2013.4 - 2015.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research
NAGAYAMA Masaharu, NAKAMURA Ken-Ichi, TERAMOTO Takashi
Grant amount：\3510000 （ Direct Cost: \2700000 、 Indirect Cost：\810000 ）
We have performed a mathematical analysis of model equations for fixed-form particle motions, as well as for one that utilizes droplet-like motions to incorporate shape deformations. In particular, droplet deformations are incorporated through the combination of a volume preserving phase-field equation within a two-component reaction diffusion system. By use of computer-aided analysis, we have also investigated the pattern dynamics within the mathematical model. We observe a parameter for which traveling spots bifurcate from stable standing spot solutions. Traveling spots, moreover, destabilize by means of a Hopf bifurcation, which leads to the appearance of an oscillatory travelling spot. We have also clarified the existence of stable elliptical-shaped and peanut-shaped equilibrium solutions.
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非周期環境における界面ダイナミクスの数理的研究とその応用
2012.4 - 2015.3
日本学術振興会 科学研究費補助金 基盤研究(C)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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Qualitative theory of nonlinear partial differential equations and the analysis of singularitiesof
Grant number：23244017 2011.4 - 2016.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)
Matano Hiroshi, NAKAMURA Ken-Ichi, FUNAKI Tadahisa, NARA Mitsunori
Grant amount：\35230000 （ Direct Cost: \27100000 、 Indirect Cost：\8130000 ）
In this research project, I made a sytematic study of the long-time behavior and stability of solutions of nonlinear partial differential equations, and also singularities arising in those solutions, by using asymptotic methods and the theory of infinite dimensional dynamical systems. More specifically, I focused on the following topics: (1) Traveling waves and spreading fronts of various kinds; (2) Qualitative study of the long-time behavior of solutions; (3) Singular limit of nonlinear diffusion equations and the associated interface motion.
These themes include free boundary problems such as the nonlinear Stefan problem. -
Mathematical analysis of the droplet motion and the particle motion with the chemical reaction.
Grant number：21340023 2009 - 2012
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
NAGAYAMA Masaharu, NAKAMURA Ken-ichi, SAITO Norikazu, NAKATA Satoshi, KITAHATA Hiroyuki, SUMINO Yutaka, OMATA Seiro
Grant amount：\17160000 （ Direct Cost: \13200000 、 Indirect Cost：\3960000 ）
Through collaborative research with experimental groups, the mathematical modeling and analysis of mechanisms for the self-propelled motion of droplets and particles under chemical reactions were investigated. The target experimental systems regard the motion of surfactant particles with stabilizing and destabilizing reactions driving their motions. By means of mathematical modeling, we clarified that the reaction order plays a central role in the oscillating phenomenon of the stabilizing system, and that the chemical product generated within the destabilizing system strongly influences the oscillation mechanism through chemical reaction. Moreover, by introducing a mathematical model for determining the mechanisms governing the motion of self-propelled grains, which oscillate spontaneously, we were able to explain the corresponding oscillation mechanism. Additionally, we analyzed the case where the particle’s geometry, here taken to be an elliptically shaped camphor disk, influences its motion.
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Validate Computation Library on Time Evolution Equations
Grant number：21540115 2009 - 2011
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
YAMAMOTO Nobito, NAKAMURA Ken-ichi, OGATA Hidenori
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
We have investigated in computer program library including validated computation techniques which give the basis of validated computation of time evolution equations, and derived a number of new approaches to numerical verification of ODEs which appear as semi-discretized equations of PDEs. The results were published in academic journals.
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不均質環境における生物種の生存競争の数理解析
2008.4 - 2012.3
日本学術振興会 科学研究費補助金 基盤研究(C)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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無限領域における非線形拡散方程式の解が生成する散逸力学系の解明に向けて
Grant number：19654030 2007 - 2008
日本学術振興会 科学研究費助成事業 萌芽研究
森田 善久, 中村 健一
Grant amount：\2200000 （ Direct Cost: \2200000 ）
無限領域における非線形拡散方程式の研究においては、進行波と呼ばれる一定波形で伝播する解の存在と安定性の研究が、中心的なテーマの一つである。しかし、解の無限次元力学系としての構造を理解するためには、進行波解の研究だけでは不十分である。進行波解を含む全域解として定義される広いクラスの解の存在について研究を発展させる必要がある。
代表者の森田は、その共同研究者とロトカーボルテラ拡散競合系の全域解の存在を数学的に証明した。この成果は、全域解の研究をシステムの反応拡散方程式にも拡げる一歩として位置づけることができ、意義がある。また、多次元空間における双安定な反応拡散方程式の進行波について、これまで見つかっていなかった新しい進行波解の存在を、森田はその共同研究者と証明した。発見した進行波解は、双安定の方程式に関わらず、単安定の反応拡散方程式に現れる進行波のように、速度について連続な族を成している。この解の構造については、未知の部分があり、更なる研究の発展が期待できる。
分担者の中村は、その共同研究者と非周期的な空間構造をもつ非有界領域上の反応拡散方程式から導かれる界面方程式について考察し、進行波解を全域解から構成するとともに、進行波解が平均速度を持つための境界形状の条件を明らかにした。これは非一様性が伝播速度に与える影響を数学的に明らかにした優れた研究である。また、中村は、均質化法のアイデアを適用することにより、環境変動が非常に小さいスケールで起こっている場合の単安定な反応拡散方程式の進行波解の伝播速度に関する公式を、従来よりも平易な方法で得られることを示した。 -
Development of numerical verification methods on evolution equations
Grant number：19540118 2007 - 2008
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
YAMAMOTO Nobito, NAKAMURA Kenichi
Grant amount：\3900000 （ Direct Cost: \3000000 、 Indirect Cost：\900000 ）
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Interface motion and blow-up phenomena in nonlinear partial differential equations
Grant number：17340044 2005 - 2007
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
MATANO Hiroshi, FUNAKI Tadahisa, WEISS Georg, TANIGUCHI Masaharu, MIZUMACHI Tetsu, NAKAMURA Ken-Ichi
Grant amount：\15620000 （ Direct Cost: \14300000 、 Indirect Cost：\1320000 ）
The aim of this research project is to make a theoretical study of various nonlinear problems related to interfacial motions and blow-up phenomena, by developing asymptotic methods based on the theory of infinite dimensional dynamical systems and stochastic methods, and also performing numerical simulations if necessary. We have obtained the following results.
(1) We have given an optimal estimate concerning the singular limit of Allen-Cahn type nonlinear diffusion equations, that has not been known previously. We also obtained similar results for FitzHugh-Nagumo systems and Lotka-Volterra competition systems.
(2) We have clarified the global dynamics of blow-up solutions in nonlinear diffusion equations. This was made possible by extending the existing theory on global attractors to the case where blow-up occurs.
(3) In nonlinear heat equations with power nonlinearity, the blow-up of solutions is classified into type I and type II, the latter being much more difficult to analyze than the former. By using a topological method based on the braid group theory, we have succeeded in determining all possible type II blow-up rates.
(4) We studied the stationary problem for the Allen-Cahn equation on the 2-dimensional space having lattice periodicity by using variational methods. We have shown that a necessary and sufficient condition for the existence of multi-layered stationary solution is that the set of single layered solutions has a gap somewhere ; in other words, this set should not be a continuum (foliation).
(5) We considered periodic traveling waves in a two-dimensional infinite strip whose boundaries are saw-tooth shaped. We determined the homogenization limit of such traveling waves as one lets the boundary undulation finer and finer.
(6) Various partial differential equations are derived from microscopic models via hydrodynamic limit. Those equations include the Stefan problem and some stochastic differential equations.
(7) Regularity of free boundaries arising in various elliptic equations such as the combustion model has bee established.
(8) Stability of V-shaped traveling wave in the equation of curvature-dependent motion has been established. -
Numerical Verification Methods for Dynamical Systems described by ODEs
Grant number：17540106 2005 - 2006
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
YAMAMOTO Nobito, NAKAMURA Ken-ichi
Grant amount：\2700000 （ Direct Cost: \2700000 ）
The present research has two purposes.
1. Investigating self-validated computation methods which have been developed so far, we select various techniques as useful tools for study of dynamical systems.
2. We develop new theoretical scheme and techniques for improvement of self-validated computation of dynamical systems.
There are several methods for self-validated computation of initial value problems of ODEs. Among them, Lohner method and TM method are well-known, which have their theoretical base on Taylor expansion and its error estimation. The main reason which extends the error in the validated computation is so-called wrapping effect. These methods use QR factorization in order to reduce the wrapping effect. We applied this technique to the Nakao's method which has been developed for validated computation of PDEs and tried to construct a numerical verification methods for ODEs based on the Nakao's method. But we found that a straightforward application does not work well. Then we have investigated
1) Reduction of the wrapping effect in the step-wise procedure by the Nakao's method.
2) How to handle the large size matrices which appear in the whole time procedure by the Nakao's method
3) Applications of the Nakao's method on boundary value problems to ODEs in order to get narrow error bound at the end point
and obtained some results on new theoretical scheme and techniques for improvement of self-validated computation of dynamical systems -
漸近解析的手法による反応拡散系の縮約とその正当化
2004.4 - 2006.3
日本学術振興会 科学研究費補助金 若手研究(B)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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金属結晶成長の数理モデルに現れる螺旋状進行波解の漸近解析的研究
2000.4 - 2002.3
日本学術振興会 科学研究費補助金 奨励研究(A)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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空間的に非一様な反応拡散方程式系に現れる進行波解の伝播制御に関する研究
1998.4 - 2000.3
日本学術振興会 科学研究費補助金 奨励研究(A)
中村 健一
Authorship：Principal investigator Grant type：Competitive
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The study of arithmetic and analytic property of automorphic forms and zeta function associated with them and numerical analysis
Grant number：09640018 1997 - 1998
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
KOJIMA Hisashi, KOMIYAMA Haruo, NUMATA Minoru, MIYAI Akio, TAYOSHI Takao, OSHIKIRI Genichi
Grant amount：\2900000 （ Direct Cost: \2900000 ）
(1) Under assumptions of the multiplicity one theorem of Hecke operators, H.Kojima deduced an explicit relation between the square of Fourier coefficients a(4n) at a. fundamental discriminant 4n of modular forms f(x)=SIGMAepsilon(-1)^kn=0,1(4), n>0 a(n)e[nzl belonging to the Kohnen's space of half integral weight (2k+1)/ and of arbitrary odd level N with primitive character x and the critical value of the zeta function of the modular form F which is the image of f under the Shimura correspondence PSI.Our methods of the proof are the same as those of Shimura. We treated the excluding case in the Shimura's paper concerning Fourier coefficients of Hilbert modular forms of half integral weight and our results gave a generalization and development of Shimura' results. Moreover, using this method, we derived an analogous results in the case of Maass wave forms of half integral weight belonging to Kohnen's spaces.
(2) Oshikiri proves that if the codimension of a bundle-like foliation F of a Riemannian manifold (M, g) with positive sectional curvature is even, then F hasa compact leaf, and that if the codimension of F is odd, then F has a leaf whose closure is a codimension (q- 1) closed submanifold of M.
(3) As ingredients for the order problem of the Riemann zeta-function, Miyai investigated alternative explicit formulas for various arithmetic exponential sums relating to the problem. On constructing the cosinus form for the Atkinson phase function f(T, n), he gave an explicit formula for |zeta(1/+iT)|^2.
(4) Tayoshi considered the equation of the vibration of a elastic string in 3-dimensional space. Supposing Hooke's law and certain Lagrangian density, on the basis of analytic mechanics, he derived a system of nonlinear partial differential equations, which, in our expectation, describes the vibration of the string. Moreover, he obtained some stationary solutions.
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