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New development in the theory of reaction-diffusion system approximation

Research Project

Project/Area Number 19740046
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Toyama

Principal Investigator

MURAKAWA Hideki  University of Toyama, 大学院・理工学研究部(理学), 助教 (40432116)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,540,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥540,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords非線形拡散問題 / 退化放物型問題 / 非線形交差拡散系 / 反応拡散系 / 数値解法ステファン問題 / 多孔質媒体流方程式 / ステファン問題 / 時間離散スキーム / 数値解法 / 交差拡散系 / アテファン問題
Research Abstract

We dealt with nonlinear diffusion problems arising in a large number of important scientific and industrial contexts. The difficulties arise from the nonlinearity of the diffusion and the problem is how to handle the nonlinearity of the diffusion. In this study, we proved that the solutions of the nonlinear diffusion problems can be approximated by those of semilinear reaction-diffusion systems which include only simple reactions and linear diffusions. This indicates that the mechanism of nonlinear diffusion might be captured by reaction-diffusion interaction. Resolving semilinear problems is typically easier than dealing with nonlinear problems. Therefore, the theory of reaction-diffusion system approximation is expected to reveal effective approaches to the study of nonlinear problems.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (40 results)

All 2010 2009 2008 2007 Other

All Journal Article (12 results) (of which Peer Reviewed: 10 results) Presentation (28 results)

  • [Journal Article] A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems2009

    • Author(s)
      H. Murakawa
    • Journal Title

      Kybernetika 45

      Pages: 580-590

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A solution of nonlinear diffusion problems by semilinear reaction-diffusi on systems2009

    • Author(s)
      Hideki Murakawa
    • Journal Title

      Kybernetika 45

      Pages: 580-590

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 放物型自由境界問題における界面の近似2009

    • Author(s)
      村川秀樹
    • Journal Title

      数理解析研究所講究録 1633

      Pages: 62-79

    • Related Report
      2009 Annual Research Report
  • [Journal Article] A regularization of a reaction-diffusion system approximation to the two-phase Stefan problem2008

    • Author(s)
      H. Murakawa
    • Journal Title

      Nonlinear Anal. 69

      Pages: 3512-3524

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A regularization of a reaction-diffusion system approximation to the two-phase Stefan problem2008

    • Author(s)
      Hideki Murakawa
    • Journal Title

      Nonlinear Analysis, Theory, Methods and Applications 69

      Pages: 3512-3524

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 自由境界問題に対する反応拡散系近似とその応用2008

    • Author(s)
      村川 秀樹
    • Journal Title

      盛岡応用数学小研究集会報告集

      Pages: 35-54

    • NAID

      120001155431

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Reaction-diffusion system approximation to degenerate parabolic systems2007

    • Author(s)
      H. Murakawa
    • Journal Title

      Nonlinearity 20

      Pages: 2319-2332

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reaction-diffusion system approximation to degenerate parabolic systems2007

    • Author(s)
      Hideki Murakawa
    • Journal Title

      Nonlinearity 20

      Pages: 2319-2332

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A relation between cross-diffusion and reaction-diffusion

    • Author(s)
      H. Murakawa
    • Journal Title

      Discrete Contin. Dyn. Syst. S (採録決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A relation between cross-diffusion and reaction-diffusion

    • Author(s)
      Hideki Murakawa
    • Journal Title

      Discrete Contin. Dynam. Systems S (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

    • Author(s)
      Hideki Murakawa
    • Journal Title

      Kybernetika (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A regularization of a reaction-diffusion system approximation to the two-phase Stefan problem

    • Author(s)
      Hideki Murakawa
    • Journal Title

      Nonlinear Analysis, Theory, Methods and Applications (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] A numerical method for cross-diffusion systems2010

    • Author(s)
      Hideki Murakawa
    • Organizer
      Reaction-Diffusion Systems : A ReaDiLab Seminar Day
    • Place of Presentation
      Universite de Paris-Sud 11, France
    • Year and Date
      2010-03-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems2010

    • Author(s)
      H. Murakawa
    • Organizer
      Spatio-Temporal Patterns from Mathematics to Biomedical Applications
    • Place of Presentation
      Archamps, France
    • Year and Date
      2010-03-16
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] 非線形交差拡散系の数値解法2010

    • Author(s)
      村川秀樹
    • Organizer
      研究集会「数値シミュレーションの理論と実践£」
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2010-02-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 半線形反応拡散と非線形拡散の関係2009

    • Author(s)
      村川秀樹
    • Organizer
      解析セミナー
    • Place of Presentation
      神戸大学
    • Year and Date
      2009-12-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] 反応-拡散の相互作用と非線形拡散2009

    • Author(s)
      村川秀樹
    • Organizer
      RIMS研究集会 第6回生物数学の理論とその応用
    • Place of Presentation
      龍谷大学セミナーハウス「ともいき荘」
    • Year and Date
      2009-11-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] 3種Lotka-Volterra競争拡散系の特異極限の解明に向けて2009

    • Author(s)
      村川秀樹
    • Organizer
      富山解析セミナー2009
    • Place of Presentation
      富山大学
    • Year and Date
      2009-10-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] 地下水の流れ,氷の融解,生物の競合2009

    • Author(s)
      村川秀樹
    • Organizer
      第3回応用数理研究会
    • Place of Presentation
      富山立山温泉ホテル雄山
    • Year and Date
      2009-08-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] A relation between reaction-diffusion interaction and cross-diffusion2009

    • Author(s)
      H. Murakawa
    • Organizer
      EQUADIFF12, Masaryk University
    • Place of Presentation
      Brno, Czech Republic
    • Year and Date
      2009-07-21
    • Related Report
      2009 Final Research Report
  • [Presentation] A relation between reaction-diffusion interaction and cross-diffusion2009

    • Author(s)
      Hideki Murakawa
    • Organizer
      EQUADIFF12
    • Place of Presentation
      Masaryk University, Brno, Czech Republic
    • Year and Date
      2009-07-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] 反応-拡散の相互作用と交差拡散の関係2009

    • Author(s)
      村川秀樹
    • Organizer
      さいたま数理解析セミナー
    • Place of Presentation
      大宮ソニックシティ
    • Year and Date
      2009-05-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] 反応-拡散の相互作用と退化拡散,交差拡散との関係2009

    • Author(s)
      村川秀樹
    • Organizer
      応用数学セミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2009-05-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] 退化拡散, 交差拡散, 反応-拡散の関係2009

    • Author(s)
      村川秀樹
    • Organizer
      小研究集会in富山「反応拡散系における諸問題2008」
    • Place of Presentation
      富山大学
    • Year and Date
      2009-01-30
    • Related Report
      2008 Annual Research Report
  • [Presentation] 非線形拡散と反応-拡散の関係2009

    • Author(s)
      村川秀樹
    • Organizer
      龍谷数理科学セミナー
    • Place of Presentation
      龍谷大学瀬田キャンパス
    • Year and Date
      2009-01-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] 非線形拡散問題に対する反応拡散系近似についてII2008

    • Author(s)
      村川秀樹
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス
    • Year and Date
      2008-12-15
    • Related Report
      2008 Annual Research Report
  • [Presentation] 放物型自由境界問題の数値解法について2008

    • Author(s)
      村川秀樹
    • Organizer
      研究集会「第10回界面ダイナミクスと数値シミュレーション」
    • Place of Presentation
      セント・キャサリンズ・カレッジ神戸インスティチュート
    • Year and Date
      2008-11-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] Nonlinear diffusion problems can be approximated by semilinear reaction-diffusion systems2008

    • Author(s)
      村川秀樹
    • Organizer
      PDE Approximations in Fast Reaction-Slow Diffus ion Scenarios
    • Place of Presentation
      Lorentz center, Leiden, The Netherlands
    • Year and Date
      2008-11-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] 交差拡散と反応-拡散の関係2008

    • Author(s)
      村川秀樹
    • Organizer
      富山解析セミナー2008
    • Place of Presentation
      富山大学
    • Year and Date
      2008-10-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] Solutions to nonlinear diffusion problems by semilinear reaction-diffusion systems2008

    • Author(s)
      Hideki Murakawa
    • Organizer
      Czech-Japanese Seminar in Applied Mathematics 2008
    • Place of Presentation
      Gokamura community center, Miyazaki, Japan
    • Year and Date
      2008-09-01
    • Related Report
      2008 Annual Research Report
  • [Presentation] 放物型自由境界問題における界面の近似2008

    • Author(s)
      村川秀樹
    • Organizer
      研究集会「パターンダイナミクスの数理とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-06-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] A solution of parabolic free boundary problems by semilinear reaction-diffusion systems2008

    • Author(s)
      H. Murakawa
    • Organizer
      Free Boundary Problems Theory and Applications
    • Place of Presentation
      KTH, Stockholm, Sweden
    • Year and Date
      2008-06-12
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] 反応拡散系近似理論の数値解析への応用2008

    • Author(s)
      村川 秀樹
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-26
    • Related Report
      2007 Annual Research Report
  • [Presentation] 半線形反応拡散系による非線形退化放物型問題の近似解法2008

    • Author(s)
      村川 秀樹
    • Organizer
      九州大学数値解析セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2008-02-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] Reaction-diffusion system approximation to free boundary problems and its application to numerical computations2007

    • Author(s)
      村川 秀樹
    • Organizer
      International Conference on Free Boundary Problems in Chiba 2007
    • Place of Presentation
      千葉大学
    • Year and Date
      2007-11-29
    • Related Report
      2007 Annual Research Report
  • [Presentation] 移動境界問題に対する反応拡散系近似とその応用2007

    • Author(s)
      村川 秀樹
    • Organizer
      盛岡応用数学小研究集会
    • Place of Presentation
      岩手大学
    • Year and Date
      2007-10-13
    • Related Report
      2007 Annual Research Report
  • [Presentation] 退化放物型方程式に対する反応拡散系近似とその応用2007

    • Author(s)
      村川 秀樹
    • Organizer
      富山解析セミナー2007
    • Place of Presentation
      富山大学
    • Year and Date
      2007-09-29
    • Related Report
      2007 Annual Research Report
  • [Presentation] Reaction-diffusion system approximation to degenerate parabolic equations and its application to numerical computations2007

    • Author(s)
      村川 秀樹
    • Organizer
      Equadiff07
    • Place of Presentation
      Vienna University of Technology, Vienna, Austria
    • Year and Date
      2007-08-08
    • Related Report
      2007 Annual Research Report
  • [Presentation] Reaction-diffusion system approximation to moving boundary problems and its application to numerical computations2007

    • Author(s)
      村川 秀樹
    • Organizer
      International Conference on Recent Developments of Numerical Schemes for Flow Problems
    • Place of Presentation
      九州大学
    • Year and Date
      2007-06-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] 退化放物型方程式に対する反応拡散系近似とその数値計算への応用2007

    • Author(s)
      村川 秀樹
    • Organizer
      数値解析ミニシンポジウ
    • Place of Presentation
      九州大学
    • Year and Date
      2007-05-29
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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