• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

On a study of a solution with a transition layer for a bistable reaction diffusion equation with a heterogeneous environment

Research Project

Project/Area Number 20740098
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionNumazu College of Technology

Principal Investigator

MATSUZAWA Hiroshi  Numazu College of Technology, 教養科, 講師 (80413780)

Project Period (FY) 2008 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords偏微分方程式 / 反応拡散方程式 / 双安定 / 遷移層 / 不変多様体 / フロント解 / 非線形偏微分方程式 / Allen-Cahn方程式
Research Abstract

In this research we study the dynamics of a single transition layer of a solution to a spatially inhomogeneous bistable reaction diffusion equation in one space dimension. The spatial inhomogeneity is given by a function of the space variable. In particular, we consider the case where this function is identically zero on an interval and study the dynamics of the transition layer on the interval. In this case the dynamics of the transition layer on the interval becomes so-called very slow dynamics. In order to analyze such a dynamics, we construct an attractive local invariant manifold giving the dynamics of the transition layer and we derive an equation describing the flow on the manifold. We also give applications of our results to two well known nonlinearities of bistable type.

Report

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

    (13 results)

All 2010 2009 2008 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (7 results)

  • [Journal Article] The motion of a transition layer for a bistable reaction diffusion equation with heterogeneous environment2010

    • Author(s)
      Shin-Ichiro Ei, Hiroshi Matsuzawa
    • Journal Title

      Discrete and Continuous Dynamical Systems 26

      Pages: 901-921

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The motion of a transition layer for a bistable reaction diffusion equation with heterogeneous environment2010

    • Author(s)
      Shin-Ichiro Ei, Hiroshi Matsuzawa
    • Journal Title

      Discrete and Continuous Dynamical Systems, Series A 26

      Pages: 901-921

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous environments2010

    • Author(s)
      Hiroshi Matsuzawa
    • Journal Title

      Discrete and continuous dynamical systems, Supplement 2009

      Pages: 516-525

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous environments2009

    • Author(s)
      Hiroshi Matsuzawa
    • Journal Title

      Discrete and Continuous Dynamical Systems supplement

      Pages: 516-525

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple stable patterns in a balanced bistable equation with heterogeneous environments

    • Author(s)
      Kazuhiro Kurata, Hiroshi Matsuzawa
    • Journal Title

      Applicable Analysis (に掲載決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple stable patterns in a balanced bistable equation with heterogeneous environments

    • Author(s)
      Kazuhiro Kurata, Hiroshi Matsuzawa
    • Journal Title

      Applicable Analysis (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] The motion of a transition layer for a bistable reaction diffusion equation with heterogeneous environment2009

    • Author(s)
      Hiroshi Matsuzawa
    • Organizer
      Equadiff 12
    • Place of Presentation
      Masaryk University(Brno, Czech Republic)
    • Year and Date
      2009-07-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Dynamics of a transition layer for a scalar bistable reaction-diffusion equation with spatially heterogeneous environments2009

    • Organizer
      Equadiff 12
    • Place of Presentation
      Masaryk University, Brno, Czech Republic
    • Year and Date
      2009-07-23
    • Related Report
      2009 Final Research Report
  • [Presentation] 空間非斉次性を含む双安定反応拡散方程式の遷移層をもつ解のダイナミクスについて2009

    • Organizer
      熊本大学応用解析セミナー
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-06-06
    • Related Report
      2009 Final Research Report
  • [Presentation] 双安定反応拡散方程式の遷移層をもつ解のダイナミクスについて2009

    • Organizer
      日本数学会2009 年度年会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-28
    • Related Report
      2009 Final Research Report
  • [Presentation] 双安定反応拡散方程式の遷移層をもつ解のダイナミクスについて2009

    • Author(s)
      松澤寛, 栄伸一郎
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学駒場キャンパス
    • Year and Date
      2009-03-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous environments2008

    • Organizer
      The 7th AIMS Conference on Dynamical Systems and Differential Equations, University of Texas at Arlington
    • Place of Presentation
      Texas, USA
    • Year and Date
      2008-05-19
    • Related Report
      2009 Final Research Report
  • [Presentation] On a solution with transition layers for a bistable reaction-diffusion equation with spatially heterogeneous enviromnents2008

    • Author(s)
      松澤寛
    • Organizer
      7th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      テキサス大学アーリントン校
    • Year and Date
      2008-05-19
    • Related Report
      2008 Annual Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi