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Global stability of multi-dimensional traveling fronts

Research Project

Project/Area Number 18540208
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionTokyo Institute of Technology

Principal Investigator

TANIGUCHI Masaharu  Tokyo Institute of Technology, 大学院・情報理工学研究科, 准教授 (30260623)

Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,150,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Keywords多次元進行波 / 安定性 / 反応拡散方程式 / 進行波 / 多次元 / 角錐型 / traveling wave / pyramidal shape / Allen-Cahn / 角錐型進行波 / Allen-Cahn方程式
Research Abstract

I studied the Allen-Cahn equation (Nagumo equation) in three-dimensional Euclidean space, and constructed pyramidal traveling front solutions and convex polyhedral traveling front solutions. I also proved that they are stable for given fluctuations.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (39 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (23 results) (of which Peer Reviewed: 17 results) Presentation (10 results) Book (5 results) Remarks (1 results)

  • [Journal Article] The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations2009

    • Author(s)
      M. Taniguchi
    • Journal Title

      Journal of Differential Equations Vol.246

      Pages: 2103-2130

    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Stability of planar waves in the Allen-Cahn equation2009

    • Author(s)
      H. Matano, M. Nara, M. Taniguchi
    • Journal Title

      Communications in Partial Differential Equations Vol.34,Issue9

      Pages: 976-1002

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pyramidal traveling fronts in the Allen-Cahn equations2009

    • Author(s)
      M. Taniguchi
    • Journal Title

      京都大学数理解析研究所講究録 1651

      Pages: 1880-2818

    • Related Report
      2009 Final Research Report
  • [Journal Article] The uniqueness and asymptotic stabilityi of pyramidal traveling fronts in the Allen-Cahn equations2009

    • Author(s)
      M.Taniguchi
    • Journal Title

      Journal of Differential Equations 246

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of planar waves in the Allen-Cahn equation2009

    • Author(s)
      H.Matano, M.Nara, M.Taniguchi
    • Journal Title

      Communications in Partial Differential Equations 34

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The uniqueness and asymptotic stability of pyramidal traveling fronts in the Allen-Cahn equations2009

    • Author(s)
      Masaharu Taniguchi
    • Journal Title

      Journal of Differential Equations 246

      Pages: 2103-2130

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of planar waves in the Allen-Cahn equation2009

    • Author(s)
      H. Matano, M. Nara, M. Taniguchi
    • Journal Title

      Communications in Partial Differential Equations (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traveling fronts of pyramidal shapes in the Allen-Cahn equations2007

    • Author(s)
      M. Taniguchi
    • Journal Title

      SIAM Journal on Mathematical Analysis Vol.39,No.1

      Pages: 319-344

    • NAID

      120006581842

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The condition on the stability of stationary lines in a curvature flow in the whole plane2007

    • Author(s)
      M. Nara, M. Taniguchi
    • Journal Title

      ournal of Differential Equations Vol.237,No.1

      Pages: 61-76

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The condition on the stability of stationary lines in a curvature flow in the whole plane2007

    • Author(s)
      M. Nara and M. Taniguchi
    • Journal Title

      Journal of Differential Equations Vol.237, No.1

      Pages: 61-76

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Traveling fronts of pyramidal shapes in the Allen-Cahn equations2007

    • Author(s)
      M. Taniguchi
    • Journal Title

      SIAM Journal on Mathematical Analysis Vol.39, No.1

      Pages: 319-344

    • NAID

      120006581842

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Traveling fronts of pyramidal shapes in the Allen-Cahn equations2007

    • Author(s)
      Masaharu Taniguchi
    • Journal Title

      SIAM Journal of Mathematical Analysis 39

      Pages: 319-344

    • NAID

      120006581842

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The condition on the stability of stationary lines in a curvature flow in the whole plane2007

    • Author(s)
      M. Nara and M. Taniguchi
    • Journal Title

      Journal of Differential Equations 237

      Pages: 61-76

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of a traveling wave in curvature flows for spatially non-decaying initial perturbations2006

    • Author(s)
      M. Nara, M. Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.14,No.1

      Pages: 203-220

    • NAID

      120006581803

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global stability of traveling curved fronts in the Allen-Cahn equations2006

    • Author(s)
      H. Ninomiya, M. Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.15,No.3

      Pages: 819-832

    • NAID

      120006581802

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Convergence to V-shaped fronts in curvature flows for spatially non-decaying initial perturbations2006

    • Author(s)
      M. Nara, M. Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol16,No.1

      Pages: 137-156

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global stability of traveling curved fronts in the Allen-Cahn equations2006

    • Author(s)
      H. Ninomiya and M. Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.15, No.3

      Pages: 819-832

    • NAID

      120006581802

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Convergence to V-shaped fronts in curvature flows for spatially non-decaying initial perturbations2006

    • Author(s)
      M.Nara, M.Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems 16・1

      Pages: 137-156

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Global stability of traveling curved fronts in the Allen-Cahn equations2006

    • Author(s)
      H.Ninomiya, M.Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems 15・3

      Pages: 819-832

    • NAID

      120006581802

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of traveling wave in curvature flows for spatially non-decaying initial perturbations2006

    • Author(s)
      M.Nara, M.Taniguchi
    • Journal Title

      Discrete and Continuous Dynamical Systems 14・1

      Pages: 203-220

    • NAID

      120006581803

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of planar waves in the Allen-Cahn equation

    • Author(s)
      H. Matano, M. Nara and M. Taniguchi
    • Journal Title

      Communications in Partial Differential Equations (印刷中)

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The condition on the stability of stationary lines in a curvature Flow in the whole plane

    • Author(s)
      M.Nara, M.Taniguchi
    • Journal Title

      Journal of Differential Equations (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Traveling fronts of pyramidal shapes in the Allen-Cahn equations

    • Author(s)
      M.Taniguchi
    • Journal Title

      SIAM J. Math. Anal. (掲載決定)

    • NAID

      120006581842

    • Related Report
      2006 Annual Research Report
  • [Presentation] Pyramidal traveling fronts in multistable reaction-diffusion equations2010

    • Author(s)
      谷口雅治
    • Organizer
      北東解析研究集会
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-02-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] Multi-dimensional traveling fronts in bistable reaction-diffusion equations2010

    • Author(s)
      M. Taniguchi
    • Organizer
      The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden University of Technology Dresden
    • Place of Presentation
      Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] 多重安定な反応拡散方程式における角錐型進行波2009

    • Author(s)
      谷口雅治
    • Organizer
      数理解析セミナー
    • Place of Presentation
      首都大学東京
    • Year and Date
      2009-12-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Allen-Cahn方程式における角錐型進行波の一意性と安定性2008

    • Author(s)
      谷口雅治
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Allen-Cahn方程式における角錐型進行波の一意性と安定性2008

    • Author(s)
      谷口雅治
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Traveling fronts of pyramidal shapes in the Allen-Cahn equations2007

    • Author(s)
      M. Taniguchi
    • Organizer
      Minisymposium "Qualitative theory of elliptic and parabolic PDEs 1" Vienna, Austria EQUADIFF 2007
    • Place of Presentation
      Vienna University of Technology
    • Year and Date
      2007-08-07
    • Related Report
      2009 Final Research Report
  • [Presentation] Traveling fronts of pyramidal shapes in the Allen-Cahn equations2007

    • Author(s)
      Masaharu Taniguchi
    • Organizer
      Equadiff2007
    • Place of Presentation
      Vienna University of Technology
    • Year and Date
      2007-08-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Traveling fronts of pyramidal shapes in the Allen-Cahn equations2007

    • Organizer
      Minisymposium "Qualitative theory of elliptic and parabolic PDEs 1" EQUADIFF 2007
    • Place of Presentation
      Vienna University of Technology
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] Traveling waves in the Allen-Cahn equations2006

    • Author(s)
      M. Taniguchi
    • Organizer
      AIMS' Sixth International Conference on Dyn. Systems, Diff. Equations and Applications University of Poitiers
    • Place of Presentation
      Poitiers
    • Year and Date
      2006-06-27
    • Related Report
      2009 Final Research Report
  • [Presentation] Allen-Cahn方程式における多次元進行波2006

    • Author(s)
      谷口雅治
    • Organizer
      日本数学会2006年年会
    • Place of Presentation
      中央大学
    • Year and Date
      2006-03-28
    • Related Report
      2009 Final Research Report
  • [Book] 現代数理科学辞典(第2版)2010

    • Author(s)
      谷口雅治
    • Publisher
      丸善株式会社
    • Related Report
      2009 Final Research Report
  • [Book] 現代数理科学事典第2版,XI-9-2 分担執筆(Page 1283-1289)2010

    • Author(s)
      谷口雅治
    • Total Pages
      7
    • Publisher
      丸善株式会社
    • Related Report
      2009 Annual Research Report
  • [Book] 数学の言葉と論理2008

    • Author(s)
      渡辺治,北野晃朗,木村泰紀,谷口雅治
    • Total Pages
      219
    • Publisher
      朝倉書店
    • Related Report
      2009 Final Research Report
  • [Book] 数学の言葉と論理2008

    • Author(s)
      渡辺治, 北野晃朗, 木村泰紀, 谷口雅治(著)
    • Publisher
      朝倉書店
    • Related Report
      2008 Self-evaluation Report
  • [Book] 数学の言葉と論理2008

    • Author(s)
      渡辺治, 北野晃朗, 木村泰紀, 谷口雅治
    • Total Pages
      219
    • Publisher
      朝倉書店
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • Related Report
      2009 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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