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Analysis of interface motion and blow-up phenomena in nonlinear partial differential equations

Research Project

Project/Area Number 20340033
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionThe University of Tokyo

Principal Investigator

MATANO Hiroshi  The University of Tokyo, 大学院・数理科学研究科, 教授 (40126165)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Kenーichi  電気通信大学, 電気通信学部, 助教 (40293120)
WEISS Georg S.  東京大学, 大学院・数理科学研究科, 准教授 (30282817)
中村 健一  電気通信大学, 電気通信学部, 助教 (40293021)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥18,720,000 (Direct Cost: ¥14,400,000、Indirect Cost: ¥4,320,000)
Fiscal Year 2010: ¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2009: ¥5,720,000 (Direct Cost: ¥4,400,000、Indirect Cost: ¥1,320,000)
Fiscal Year 2008: ¥6,890,000 (Direct Cost: ¥5,300,000、Indirect Cost: ¥1,590,000)
Keywords非線形問題 / 非線形偏微分方程式 / 進行波 / 特異性 / 界面運動 / 解の爆発 / 電気生理学 / 非線形現象 / 安定性 / 特異極限 / 組みひも群 / 爆発現象 / 均質化極限
Research Abstract

This research project deals with such themes as (1) traveling waves in nonlinear diffusion equations, (2) singular limit of nonlinear diffusion equations and interface motion, (3) blow-up in nonlinear heat equations, (4) mathematical analysis of 3D cellular electrophysiological model. The theme (4) was added after the program began. In theme (1), we studied, among other things, traveling waves colliding with obstacles, the stability of planar waves, and the problem of maximizing traveling wave speeds. In theme (3) we studied, among other things, classification of blow-up in Sobolev superlinear heat equations, and an application the theory of braid groups to the dead-core problem.

Report

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

    (40 results)

All 2011 2010 2009 2008 Other

All Journal Article (22 results) (of which Peer Reviewed: 22 results) Presentation (18 results)

  • [Journal Article] Threshold and generic type I behaviors for a supercritical nonlinear heat equation2011

    • Author(s)
      H.Matano, F.Merle
    • Journal Title

      J.Functional Anal. 261

      Pages: 716-748

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and uniqueness of a three-dimensional model of cellular electrophysiology2011

    • Author(s)
      H.Matano, Y.Mori
    • Journal Title

      Discrete and Continuous Dynamical Systems, Ser.A 29

      Pages: 1573-1636

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Threshold and generic type I behaviors for a supercritical nonlinear heat equation2011

    • Author(s)
      H.Matano, F.Merle
    • Journal Title

      J.Functional Analysis

      Volume: 掲載確定

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and uniqueness of a three-dimensional model of cellular electrophysiology2011

    • Author(s)
      H.Matano, Y.Mori
    • Journal Title

      Discrete and Continuous Dynamical Systems, Ser.A

      Volume: 29 Pages: 1573-1636

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An application of braid group theory to the finite time dead-core rate2010

    • Author(s)
      J.-S.Guo, H.Matano, C.-C.Wu
    • Journal Title

      J.Evolution Equations 10

      Pages: 835-855

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation2010

    • Author(s)
      M.Alfaro, H.Garcke, D.Hilhorst, H.Matano, R.Schaetzle
    • Journal Title

      Proc.Royal Soc.Edinburgh, Ser.A 140

      Pages: 673-706

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction- diffusion equations2010

    • Author(s)
      X.Liang, X.Lin, H.Matano
    • Journal Title

      Trans.Amer.Math.Soc. 462

      Pages: 5605-5633

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Convergence and sharp thresholds for propagation in nonlinear diffusion problems2010

    • Author(s)
      Y.Du, H.Matano
    • Journal Title

      J.Eur.Math.Soc. 12

      Pages: 279-312

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] An application of braid group theory to the finite time dead-core rate2010

    • Author(s)
      J.-S.Guo, H- Matano, C.-C.Wu
    • Journal Title

      J.Evolution Equations

      Volume: 10 Pages: 835-855

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation2010

    • Author(s)
      M.Alfaro, H.Garcke, D.Hilhorst, H.Matano, R.
    • Journal Title

      Proc.Royal Society of Edinburgh, Ser.A

      Volume: 140 Pages: 673-706

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A variational problem associated with the minimal speed of travelling waves for spatially periodic reaction-diffusion equations2010

    • Author(s)
      X.Liang, X.Lin, H.Matano
    • Journal Title

      Transactions of American Mathematical Society

      Volume: 462 Pages: 5605-5603

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence and sharp thresholds for propagation in nonlinear diffusion problems2010

    • Author(s)
      Y.Du, H.Matano
    • Journal Title

      Journal of European Mathematical Society

      Volume: 12 Pages: 279-312

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The radius of vanishing bubbles in equivariant harmonic map flow from D2 to S22009

    • Author(s)
      S.B.Angenent, J.Hulshof, H.Matano
    • Journal Title

      SIAM J.Math.Anal. 41

      Pages: 1121-1137

    • Related Report
      2010 Final 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

      Comm.Partial Differential Equations 34

      Pages: 976-1002

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of Type I and Type II behaviors for a supercritical nonlinear heat equation2009

    • Author(s)
      H.Matano, F.Merle
    • Journal Title

      J.Funct.Anal. 256

      Pages: 992-1064

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bistable travelling waves around an obstacle2009

    • Author(s)
      H.Berestycki, F.Hamel, H.Matano
    • Journal Title

      Comm.Pure Appl.Math. 62

      Pages: 729-788

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion2009

    • Author(s)
      R.Monneau, G.S.Weiss
    • Journal Title

      Ann.Inst.Henri Poincare 26

      Pages: 1207-1222

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The radius of vanishing bubbles in equivariant harmonic map flow from D^2 to S^22009

    • Author(s)
      S.B.Angenent, J.Hulshof, H.Matano
    • Journal Title

      SIAM J.Math.Anal. 41

      Pages: 1121-1137

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pulsating traveling waves in the singular limit of a reaction-diffusion system in solid combustion2009

    • Author(s)
      R.Monneau, G.S.Weiss
    • Journal Title

      Annales de l'Institut Henri Poincare 26

      Pages: 1207-1222

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of Type I and Type II behaviors for a supercritical nonlinear heat equation2009

    • Author(s)
      H.Matano and F.Merle
    • Journal Title

      J.Funct.Anal 256

      Pages: 992-1064

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bistable traveling waves around an obstacle2009

    • Author(s)
      H.Berestycki, F.Hamel and H.Matano
    • Journal Title

      Comm.Pure Appl.Anal 62

      Pages: 729-788

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence and sharp thresholds for propagation in nonlinear diffusion problems

    • Author(s)
      Y.Du and H.Matano
    • Journal Title

      J.European Mathematical Society (掲載確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Global solutions for a 3D model of cellular electrophysiology2011

    • Author(s)
      俣野博
    • Organizer
      Conference on Far From Equilibrium Dynamics
    • Place of Presentation
      京都大学
    • Year and Date
      2011-01-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Global solutions for a 3D model of cellular electrophysiology2011

    • Author(s)
      俣野博
    • Organizer
      Conference on Far-From-Equilibrium-Dynamics 2011
    • Place of Presentation
      京都大学
    • Year and Date
      2011-01-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] On supercritical blow-up for the nonlinear heat equation2010

    • Author(s)
      俣野博
    • Organizer
      Workshop on Qualitative Studies of Evolution PDEs
    • Place of Presentation
      セルジポントワーズ大学(フランス)
    • Year and Date
      2010-12-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Front propagation in hyperbolic space2010

    • Author(s)
      俣野博
    • Organizer
      Conference on Interface Motion and Traveling Waves in Reaction Diffusion Equations
    • Place of Presentation
      同済大学(中国)
    • Year and Date
      2010-10-14
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Comparison of the rescaled energy for supercritical nonlinear heat equations2010

    • Author(s)
      俣野博
    • Organizer
      爆発に関する第4回日欧会議
    • Place of Presentation
      ライデン大学(オランダ)
    • Year and Date
      2010-09-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Comparison of the rescaled energy for supercritical nonlinear heat equations2010

    • Author(s)
      俣野博
    • Organizer
      4th Euro-Japanese Conference on Blow-up
    • Place of Presentation
      ライデン大学(オランダ)
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] Front propagation on nonlinear diffusion equation on hyperbolic space2010

    • Author(s)
      俣野博
    • Organizer
      Workshop on Recent Advances on de Giorgi's Conjecture and the Study of Entire Solutions of Nonlinear Scalar Equations
    • Place of Presentation
      バンフセンター(カナダ)
    • Year and Date
      2010-08-09
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Threshold and generic type I behaviors for a supercritical nonlinear heat equation2010

    • Author(s)
      俣野博
    • Organizer
      8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      ドレスデン工科大学(ドイツ)
    • Year and Date
      2010-05-26
    • Related Report
      2010 Final Research Report
  • [Presentation] Threshold and generic type I behaviors for a supercritical nonlinear heat equation2010

    • Author(s)
      俣野博
    • Organizer
      8th AIMS International Conference on "Dynamical Systems, Differential Equations and Applications"
    • Place of Presentation
      ドレスデン大学(ドイツ)
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] Global solutions for a 3D model of cellular electrophysiology2010

    • Author(s)
      俣野博
    • Organizer
      ReaDiLab Conference: Spatio-Temporal Patterns
    • Place of Presentation
      Archamps学術センター(フランス)
    • Year and Date
      2010-03-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Global solutions for a three-dimensional model of cellular electrophysiology2010

    • Author(s)
      H.Matano
    • Organizer
      Japan-French ReaDiLab meeting on Spatio-Temporal Patterns from Mathematics to Biomedical Applications
    • Place of Presentation
      Archamps(フランス)
    • Year and Date
      2010-03-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Front propagation under ergodic perturbations; Front progapation in the hyperbolic space2010

    • Author(s)
      俣野博
    • Organizer
      Conference on Nonlinear PDE's
    • Place of Presentation
      ポハン工科大学(韓国)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Homogenization limit of reccurent traveling waves in a 2D cylinder with saw-toothed boundary2009

    • Author(s)
      俣野博
    • Organizer
      非線形楕円型と放物型偏微分方程式に関する第2回日本チリ合同会議
    • Place of Presentation
      明治大学
    • Year and Date
      2009-12-05
    • Related Report
      2010 Final Research Report
  • [Presentation] Homogenization limit of reccurent traveling waves in a 2D cylinder with saw-toothed boundary2009

    • Author(s)
      H.Matano
    • Organizer
      The Second Chile-Japan Workshop on Nonlinear Elliptic and Parabolic PDEs
    • Place of Presentation
      明治大学(東京)
    • Year and Date
      2009-12-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] Front propagation in spatially ergodic media2009

    • Author(s)
      俣野博
    • Organizer
      Conference on Mathematical Challenges Motivated by Multi-Phase Materials
    • Place of Presentation
      Anogia学術村(ギリシャ)
    • Year and Date
      2009-06-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Front propagation in spatially ergodic media2009

    • Author(s)
      H.Matano
    • Organizer
      Conference on Mathematical Challenges Motivated by Multi-Phase Materials
    • Place of Presentation
      Anogia(ギリシャ)
    • Year and Date
      2009-06-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Mathematical Analysis of a 3D Model of Cellular Electrophysiology2009

    • Author(s)
      H.Matano
    • Organizer
      Workshop on Reaction-Diffusion Systems : Modelling and Analysis
    • Place of Presentation
      Orsay(フランス)
    • Year and Date
      2009-06-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Front propagation in spatially stratified environments2008

    • Author(s)
      俣野博
    • Organizer
      国際会議Differential Equations and Applications to Mathematical Biology
    • Place of Presentation
      Le Havre(フランス)
    • Year and Date
      2008-06-24
    • Related Report
      2008 Annual Research Report

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

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