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Classification of nonlinearities of reaction-diffusion systems from a dynamical viewpoint

Research Project

Project/Area Number 20540144
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionRyukoku University

Principal Investigator

NINOMIYA Hirokazu  Ryukoku University, 理工学部, 准教授 (90251610)

Co-Investigator(Renkei-kenkyūsha) IIDA Masato  宮崎大学, 工学部, 教授 (00242264)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords反応拡散系 / 爆発問題 / 解の大域的存在 / 急速反応極限 / 進行波解 / 全域解 / 反応律速極限
Research Abstract

To classify the nonlinearities of reaction-diffusion systems, we studied the following researches. We derive the limit problem from some reaction-diffusion systems by using the fast reaction limit and discuss the relationship between the degeneracy of nonlinearity and the limit problem. We also constructed non-planar traveling waves of Allen-Cahn equations or the free boundary value problem which comes from some reaction-diffusion system, which are of finger type and of spot type. We also studied the imperfect bifurcation of some elliptic problem under the perturbation of the domain.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (30 results)

All 2011 2010 2009 2008 Other

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (17 results) Remarks (1 results)

  • [Journal Article] Fast reaction limit of a three-component reaction-diffusion system2011

    • Author(s)
      H.Murakawa, H.Ninomiya
    • Journal Title

      Journal of Mathematical Analysis and Applications 379(1)

      Pages: 150-170

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fast reaction limit of a three-component reaction-diffusion system2011

    • Author(s)
      H.Murakawa, H.Ninomiya
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 379 Pages: 150-170

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traveling wave solutions and entire solutions to reaction-diffusion equations2010

    • Author(s)
      Y.Morita, H.Ninomiya
    • Journal Title

      SUGAKU Expositions. 23(2)

      Pages: 213-233

    • NAID

      130004558838

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Imperfect bifurcations in nonlinear elliptic equations on spherical caps2010

    • Author(s)
      C.Bandle, Y.Kabeya, H.Ninomiya
    • Journal Title

      Communications on Pure and Applied Analysis 9(5)

      Pages: 1189-1208

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of stabilized propagating wave segments in wave front interaction model2010

    • Author(s)
      J.-S.Guo, H.Ninomiya, J.-C.Tsai
    • Journal Title

      Physica D : Nonlinear Phenomena 239(3-4)

      Pages: 230-239

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Imperfect bifurcations in nonlinear elliptic equations on spherical caps2010

    • Author(s)
      C.Bandle, Y.Kabeya, H.Ninomiya
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 9 Pages: 1189-1208

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of stabilized propagating wave segments in wave front interaction model2010

    • Author(s)
      J.-S.Guo, H.Ninomiya, J.-C.Tsai
    • Journal Title

      Physica D Nonlinear Phenomena 239

      Pages: 230-239

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fast Reaction Limit of Competition-Diffusion Systems2009

    • Author(s)
      D.Hilhorst, M.Mimura, H.Ninomiya
    • Journal Title

      C.M.Dafermos and Milan Pokorny(editors : Evolutionary Equations, Handbook of Differential Equations, Hungary: North-Holland) 5

      Pages: 105-168

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fast Reaction Limit of Competition-Diffusion Systems2009

    • Author(s)
      D.Hilhorst, M.Mimura, H.Ninomiya
    • Journal Title

      Evolutionary Equations, Vol 5, Handbook of Differential Equations (C.M.Dafermos and Milan Pokorny, editors)

      Pages: 105-168

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monostable-type traveling waves of bistable reaction-diffusion equations in the multi-dimensional space2008

    • Author(s)
      Y.Morita, H.Ninomiya
    • Journal Title

      Bulletin of the Institute of Mathematics. 3(4)

      Pages: 567-584

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relative compactness in L^p of solutions of some 2m components competition-diffusion systems2008

    • Author(s)
      D.Hilhorst, M.Iida, M.Mimura, H.Ninomiya
    • Journal Title

      Discrete and continuous dynamical systems. 21(1)

      Pages: 233-244

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Monotone-type traveling waves of bistable reaction-diffusion equations in the multi-dimensional space2008

    • Author(s)
      Y. Morita, H. Ninomiya
    • Journal Title

      Bulletin of the Institute of Mathematics 3

      Pages: 567-584

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Non-planar traveling waves of reaction-diffusion equations2011

    • Author(s)
      二宮広和
    • Organizer
      19th Workshop on Differential Equations
    • Place of Presentation
      National Cheng Kung University, Taiwan
    • Related Report
      2010 Final Research Report
  • [Presentation] Non-planar traveling waves of reaction-diffusion equations2010

    • Author(s)
      二宮広和
    • Organizer
      Nonlinear Analysis and Integrable Systems非線形解析と可積分系数理
    • Place of Presentation
      Ryukoku University, Kyoto
    • Related Report
      2010 Final Research Report
  • [Presentation] Traveling waves of Allen-Cahn equations, Applied Mathematics Forum, Tohoku University2010

    • Author(s)
      二宮広和
    • Organizer
      Mini-workshop on "Modeling, Simulations and Analysis of Biological Pattern Formation"
    • Place of Presentation
      Heanel Sendai
    • Related Report
      2010 Final Research Report
  • [Presentation] Non-planar traveling waves of reaction-diffusion equations2010

    • Author(s)
      二宮広和
    • Organizer
      Workshop on Pattern formation in Chemical and Biological Systems
    • Place of Presentation
      Eotvos University, Budapest, Hungry
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Stacked fronts for cooperative systems with equal diffusions2010

    • Author(s)
      二宮広和
    • Organizer
      Reaction-Diffusion Systems: Experiments, Modeling, and Analysis
    • Place of Presentation
      Universite de Paris-Sud 11, Orsay
    • Related Report
      2010 Final Research Report
  • [Presentation] Traveling waves of Allen-Cahn equation2010

    • Author(s)
      二宮広和
    • Organizer
      Workshop on Interface motion and Traveling Waves in Reaction Diffusion Equations
    • Place of Presentation
      Department of Mathematics, Tongji University, Shanghai, China
    • Related Report
      2010 Final Research Report
  • [Presentation] Traveling waves in the various shapes2010

    • Author(s)
      二宮広和
    • Organizer
      AIMS conference
    • Place of Presentation
      Dresden
    • Related Report
      2010 Final Research Report
  • [Presentation] On the diffusion-preventing blowup of reaction-diffusion equations, Spatio-Temporal Patterns from Mathematics to Biomedical Applications2010

    • Author(s)
      二宮広和
    • Organizer
      Japanese French Meeting ReaDiLab 2010
    • Place of Presentation
      ARCHAMPS, FRANCE
    • Related Report
      2010 Final Research Report
  • [Presentation] Traveling segments and rotating waves of wave front interaction model2010

    • Author(s)
      二宮広和
    • Organizer
      第27回九州における偏微分方程式研究集会
    • Place of Presentation
      九州大学
    • Related Report
      2010 Final Research Report
  • [Presentation] 最大値原理からみたパターン形成2009

    • Author(s)
      二宮広和
    • Organizer
      現象数理 : 冬の学校2009 パターンダイナミクス 1-2-3
    • Place of Presentation
      明治大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Some entire solutions of reaction-diffusion equations2009

    • Author(s)
      二宮広和
    • Organizer
      The Second Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDEs
    • Place of Presentation
      Meiji University
    • Related Report
      2010 Final Research Report
  • [Presentation] Propagating waves in wave front interaction model2009

    • Author(s)
      二宮広和
    • Organizer
      非線形発展方程式と現象の数理
    • Place of Presentation
      RIMS Kyoto University, Kyoto
    • Related Report
      2010 Final Research Report
  • [Presentation] Traveling segments in excitable media2009

    • Author(s)
      二宮広和
    • Organizer
      Reaction-diffusion systems : Modeling and analysis
    • Place of Presentation
      Universite de Paris-Sud 11, Orsay
    • Related Report
      2010 Final Research Report
  • [Presentation] Blowup in reaction-diffusion equations2009

    • Author(s)
      二宮広和
    • Organizer
      6th European Conference on Elliptic and Parabolic Problems
    • Place of Presentation
      Gaeta, Italy
    • Related Report
      2010 Final Research Report
  • [Presentation] Conditions for the blowup of solutions to a reaction-diffusion equation2008

    • Author(s)
      Hirokazu Ninomiya
    • Organizer
      3^<rd> Euro-Japanese workshop on blowup
    • Place of Presentation
      東北大学(仙台)
    • Year and Date
      2008-09-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Fast reaction limit and Turing's instability2008

    • Author(s)
      二宮広和
    • Organizer
      PDE approximations in Fast reaction-Slow diffusion scenarios
    • Place of Presentation
      Lorentz center, Leiden
    • Related Report
      2010 Final Research Report
  • [Presentation] Conditions for the blowup of solutions to a reaction diffusion equations2008

    • Author(s)
      二宮広和
    • Organizer
      Third Euro-Japanese workshop on Blowup
    • Place of Presentation
      Tohoku University
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.meiji.ac.jp/~ninomiya/

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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