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KUWAMURA MasatakaGraduate School of Human Development and Environment / Department of Human Environmental ScienceProfessor
Research activity information
■ Award- Sep. 2009 日本応用数理学会, 日本応用数理学会論文賞, Japan Journal of Industrial and Applied Mathematics, vol 25, pp.281-303 (2008) に掲載された論文
- Elsevier BV, 2025, Journal of Differential Equations, 440, 113430[Refereed]Scientific journal
- 2024, Nonlinearity, 37, 115013, EnglishSingle Transition Layer in Mass-Conserving Reaction-Diffusion Systems with Bistable Nonlinearity[Refereed]Scientific journal
- Springer Science and Business Media LLC, 2022, Journal of Mathematical Biology, 84(4) (4), 22, English[Refereed]Scientific journal
- 2018, SIAM Journal on Applied Mathematics, 78(6) (6), 3238 - 3257, EnglishDynamics of localized unimodal patterns in reaction-diffusion systems for cell polarization by extracellular signaling[Refereed]Scientific journal
- 2017, CHAOS, 27(3) (3), 012908, English[Refereed]Scientific journal
- 2015, Journal of Mathematical Biology, 71, 125 - 149, EnglishTuring instabilities in prey-predator systems with dormancy of predators[Refereed]Scientific journal
- 2015, Physical Review E, 92, 012908, EnglishPerturbations and dynamics of reaction-diffusion systems with mass conservation[Refereed]Scientific journal
- 2014, Funkcialaj ekvacioj. Serio internacia, 57(2) (2), 339 - 350, EnglishStability of coexisting equilibrium of prey-predator systems with dormancy of predators[Refereed]Scientific journal
- 2012, Journal of Biological Dynamics, 6(2) (2), 267 - 276, English[Refereed]Scientific journal
- 2011, Population Ecology, 53(2) (2), 341 - 350, English[Refereed]Scientific journal
- 2011, SIAM Journal on Applied Mathematics, 71(1) (1), 169 - 179, English[Refereed]Scientific journal
- Informa UK Limited, 2010, Journal of Biological Dynamics, 4(3) (3), 248 - 257[Refereed]Scientific journal
- 2009, CHAOS, 19, 043121, EnglishMixed-mode oscillations and chaos in a prey-predator system with dormancy of predators[Refereed]Scientific journal
- 2009, Journal of Mathematical Biology, 58(3) (3), 459 - 479, English[Refereed]Scientific journal
- 2008, Japan Journal of Industrial and Applied Mathematics, 25, 281 - 303, EnglishDeviation from the predicted wavenumber in a mode selection problem for the Turing patterns[Refereed]Scientific journal
- 2007, Advanced Studies in Pure Mathematics, 47, 635 - 646, EnglishThe Hamiltonian formalism in reaction-diffusion systems[Refereed]Scientific journal
- Mar. 2006, 応用数理, 16(1) (1), 17 - 26, JapaneseHamiltonian Formalism in Pattern Formation Problems in Dissipative Systems[Refereed]Scientific journal
- 2006, Journal of Differential Equations, 230, 446 - 464, EnglishKrein's formula for indefinite multipliers in linear periodic Hamiltonian systems[Refereed]Scientific journal
- 2005, SIAM Journal on Applied Mathematics, 65(2) (2), 618 - 643, English[Refereed]Scientific journal
- 2005, Physica D, 207, 171 - 219, EnglishA variational approach to singular perturbation problems in reaction-diffusion systems[Refereed]Scientific journal
- 2003, Physica D, 175, 185 - 195, EnglishThe Eckhaus and zigzag instability criteria in gradient/skew-gradient dissipative systems[Refereed]Scientific journal
- 2001, Japan Journal of Industrial and Applied Mathematics, 187, 739 - 768, EnglishA perspective of renormalization group approaches[Refereed]Scientific journal
- 1996, SIAM Journal on Mathematical Analysis, 27(5) (5), 1311 - 1335, EnglishThe stability of roll solutions of the two-dimensional Swift-Hohenberg equation and the phase-diffusion equation[Refereed]Scientific journal
- 1994, Journal of Dynamics and Differential Equations, 6, 185 - 225, EnglishPhase dynamics method with applications to the Swift-Hohenberg equation[Refereed]Scientific journal
- 1992, Japan Journal of Industrial and Applied Mathematics, 9, 35 - 77, EnglishVery slow dynamics for some reaction-diffusion system with activator-inhibitor type[Refereed]Scientific journal
■ Books And Other Publications
- Single work, 裳華房, Nov. 2018, Japanese応用解析概論Textbook
- Single work, 裳華房, Feb. 2016, Japanese線形代数学入門Textbook
- Single work, 共立出版, Jan. 2015, Japaneseパターン形成と分岐理論Scholarly book
- Single work, 裳華房, Nov. 2008, Japanese微分積分入門Textbook
- RIMS 共同研究(公開型) 常微分方程式の定性的理論の構築とその汎用性の探究, Oct. 2024, JapaneseSingle transition layer in mass-conserving reaction-diffusion systems with bistable nonlinearity[Invited]Oral presentation
- Turing Symposium on Morphogenesis 2024, Feb. 2024, EnglishPeriodic solutions of mass-conserving reaction-diffusion systems and their perturbed systems[Invited]Invited oral presentation
- 反応拡散系パターンダイナミクスの新展開, Jun. 2023, Japanese保存量をもつ反応拡散方程式系における特異摂動問題について[Invited]Invited oral presentation
- OCAMI共同研究 「反応拡散方程式と非線形分散型方程式の解の挙動」, Feb. 2023保存量をもつ反応拡散方程式系における特異摂動問題について[Invited]Invited oral presentation
- Okayama Workshop on Partial Differential Equations, Oct. 2022保存量をもつ反応拡散方程式系における特異摂動問題について[Invited]Invited oral presentation
- 明治大学MIMS共同研究集会「幾何学・連続体力学・情報科学の交差領域の探索」, Dec. 2020細胞極性化に関連する微分方程式の解の性質について[Invited]
- OCAMI共同研究「反応拡散方程式と非線形分散型方程式の解の挙動」, Feb. 2020, Japanese保存量をもつ反応拡散系における特異摂動の例について[Invited]Invited oral presentation
- The 43rd Sapporo Symposium on Partial Differential Equations, Aug. 2018, English, International conferenceDynamics of localized patterns in reaction-diffusion systems for cell polarization by extracellular signaling[Invited]Invited oral presentation
- 2017年度応用数学合同研究集会, Dec. 2017, Japanese, Domestic conference保存量をもつ反応拡散系におけるパルス状局在解の挙動についてOral presentation
- JSMB2016, Sep. 2016, English, Fukuoka, Japan, International conferenceDiffusion driven destabilization of a spatially homogeneous limit cycle in reaction-diffusion systemsOral presentation
- ICIAM2015, Aug. 2015, English, Beijing, China, International conferenceConservation breaking dynamics in reaction-diffusion systems[Invited]Oral presentation
- 生物数学の理論とその応用, Sep. 2014, Japanese, 京都大学数理解析研究所, Domestic conference捕食者の休眠を伴う prey-predator 系に現れるTuring 不安定性についてOral presentation
- 3rd Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's, Sep. 2013, English, Tokyo, International conferenceTuring patterns in prey-predator systems with dormancy of predators[Invited]Oral presentation
- The 7th East Asia SIAM Conference, Jun. 2011, English, Waseda University, Kitakyushu Campus, International conferenceDormancy of predators in prey-predator systemsOral presentation
- The second China-Japan Colloquim of Mathematical Biology, Aug. 2008, English, Okayama University, International conferenceMathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cellsOral presentation
- 日本数学会春期応用数学分科会特別講演, 2004, Japanese, 日本数学会, 筑波,, Domestic conference散逸系におけるパターン選択問題について[Invited]Invited oral presentation
■ Research Themes
- 日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 01 Apr. 2024 - 31 Mar. 2029特異摂動法の新しい理論と応用ー細胞極性に関する反応拡散方程式モデルの数理解析ー
- Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2016 - Mar. 2023Mass-conserving reaction-diffusion systems and their perturbationIn this research, I studied mass-conserving reaction-diffusion systems which are mathematical models for the polarity formation of cells. First, I investigated the dynamics of a localized unimodal pattern in mass-conserving reaction-diffusion systems, and provided mathematical characterizations of the motion of the localized unimodal pattern. Next, I investigated the oscillatory dynamics and bifurcation structure of a mass-conserving reaction-diffusion system with bistable nonlinearity, and showed that it exhibits four different spatiotemporal patterns including two types of oscillatory patterns, My research was based on a joint work with Professors Hirofumi Izuhara (Miyazaki),Sungrim Seirin-Lee (Kyoto) and Shin-Ichiro Ei (Hokkaido), and my results were published in Chaos, vol.27 (2017), SIAM Journal on Applied Mathematics, vol.78 (2018) and Journal of Mathematical Biology, vol.84 (2022).
- Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2010 - Mar. 2014Pattern dynamics in dissipative systems and their related topicsWe investigated properties of solutions of prey-predator system with dormant predators. Moreover, we proposed a mathematical model for the differentiation and proliferation of Drosophila intestinal stem cells.
- 科学研究費補助金/基盤研究(C), 2010Competitive research funding
- Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, 2006 - 2009Hamiltonian structure in the pattern selection problems of dissipative systemsWe studied the gradient/skew-gradient structure that enables us to apply the Hamiltonian formalism for studying the stability of stationary solutions in reaction-diffusion systems in various pattern formation problems. Moreover, we studied the stabilizing effect of dormancy of predators on the population dynamics of prey-predator systems.
- 科学研究費補助金/基盤研究(C), 2008Competitive research funding
- 日本学術振興会, 科学研究費助成事業, 萌芽研究, 神戸大学, 2003 - 2005勾配・歪勾配構造をもつ散逸系における時空間周期パターンの解析勾配・歪勾配構造は散逸系にハミルトン構造を自然に導くものである。この構造をもつ散逸系においては、時空間周期パターンの安定性は極めて単純で自然な公式によって決定される。この結果は、柳田教授との共著論文として、Physica D 175(2003)pp.185-195において発表した。また、多数の安定な空間周期パターンのうち、現実的にどの空間周期をもったパターンが最も高い確率で現れるのかというパターン選択問題を、勾配・歪勾配構造をもつ散逸系の場合に調べた。とくにパターン選択の基本原理ではないかと予想されている「臨界安定性仮説」を本研究の補助金によって購入したパソコンを利用した数値実験によって検証した。幸運にも、2004年度の春の日本数学会応用数学分科会(筑波大学)の特別講演者に推薦されたこともあり、この結果を学会の特別講演の形で発表することができた。この結果をまとめた論文は、SIAM J.Appl.Math.65(2005)pp.618-643において発表した。本年度は、これらの一連の研究に引き続いて、九州大学数理学研究院の栄伸一郎教授と龍谷大学理工学部の森田善久教授との共同研究を行い、反応拡散方程式に現れる特異摂動問題をハミルトン構造の視点から調べて、その成果をPhysica D 207(2005)pp.171-219で発表することができた。また、2005年度の秋の日本数学会応用数学分科会(岡山大学)でも研究発表することができた。一方、研究分担者の小川は、ミシャイコフ教授らのグループとの共同研究でSwift-Hohenberg方程式の分岐ダイアグラムを詳細に調べることに成功した。その結果は、SIAM J.Appl.Dyn.Sys.4(2005)pp.1-31において発表された。
- 科学研究費補助金/基盤研究(C), 2005Competitive research funding
- 科学研究費補助金/基盤研究(B), 2005Competitive research funding
- 科学研究費補助金/基盤研究(C), 2005Competitive research funding