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Qualitative theory of nonlinear partial differential equations and the analysis of singularitiesof

Research Project

Project/Area Number 23244017
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

Matano Hiroshi  東京大学, 数理(科)学研究科(研究院), 教授 (40126165)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Ken-Ichi  金沢大学, 数物科学系, 准教授 (40293120)
FUNAKI Tadahisa  東京大学, 大学院数理科学研究科, 教授 (60112174)
Co-Investigator(Renkei-kenkyūsha) NARA Mitsunori  岩手大学, 人文社会学部, 准教授 (90512161)
Project Period (FY) 2011-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥35,230,000 (Direct Cost: ¥27,100,000、Indirect Cost: ¥8,130,000)
Fiscal Year 2014: ¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2013: ¥7,280,000 (Direct Cost: ¥5,600,000、Indirect Cost: ¥1,680,000)
Fiscal Year 2012: ¥7,150,000 (Direct Cost: ¥5,500,000、Indirect Cost: ¥1,650,000)
Fiscal Year 2011: ¥11,440,000 (Direct Cost: ¥8,800,000、Indirect Cost: ¥2,640,000)
Keywords非線形偏微分方程式 / 定性的理論 / 進行波 / 界面運動 / 解の爆発 / 特異極限 / 自由境界問題 / 非線形拡散方程式 / 漸近挙動 / 広がり波面 / 拡散方程式 / 国際研究者交流(イタリア) / 国際研究者交流(中国) / 国際研究者交流(オーストラリア) / 順序保存力学系 / 国際研究者交流(フランス) / 国際情報交換(中国) / 平面波 / 安定性 / 無限次元力学系 / エルゴード性 / 国際研究者交流(フランス) / 国際情報交換(イタリア)
Outline of Final Research Achievements

In this research project, I made a sytematic study of the long-time behavior and stability of solutions of nonlinear partial differential equations, and also singularities arising in those solutions, by using asymptotic methods and the theory of infinite dimensional dynamical systems. More specifically, I focused on the following topics: (1) Traveling waves and spreading fronts of various kinds; (2) Qualitative study of the long-time behavior of solutions; (3) Singular limit of nonlinear diffusion equations and the associated interface motion.
These themes include free boundary problems such as the nonlinear Stefan problem.

Report

(5 results)
  • 2015 Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (51 results)

All 2016 2015 2014 2013 2012 2011 Other

All Int'l Joint Research (4 results) Journal Article (16 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 16 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (29 results) (of which Int'l Joint Research: 6 results,  Invited: 29 results) Funded Workshop (2 results)

  • [Int'l Joint Research] パリ南大学/CNRS/フランス高等社会科学院(フランス)

    • Related Report
      2014 Annual Research Report
  • [Int'l Joint Research] University of Warwick(英国)

    • Related Report
      2014 Annual Research Report
  • [Int'l Joint Research] 淡江大学/台南国立大学(台湾)

    • Related Report
      2014 Annual Research Report
  • [Int'l Joint Research] ローマ大学(La Sapienza)(イタリア)

    • Related Report
      2014 Annual Research Report
  • [Journal Article] On the large time behavior of the solutions of a nonlocal ordinary differential equation with mass conservation2016

    • Author(s)
      D. Hilhorst, H. Matano, T.N. Nguyen and H. Weber
    • Journal Title

      J. Dynamics and Differential Equations

      Volume: 掲載確定 Issue: 3-4 Pages: 707-731

    • DOI

      10.1007/s10884-015-9465-7

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On a free boundary problem for the curvature flow with driving force2016

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

      Archive for Rational Mechanics and Analysis

      Volume: 219 Issue: 3 Pages: 1207-1272

    • DOI

      10.1007/s00205-015-0920-8

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Front propagation for nonlinear diffusion equations on the hyperbolic space2015

    • Author(s)
      H. Matano, F. Punzo and A. Tesei
    • Journal Title

      J. European Mathematical Society

      Volume: 17 Issue: 5 Pages: 1199-1227

    • DOI

      10.4171/jems/529

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Existence and uniqueness of solutions to stochastic Rayleigh-Plesset equations2015

    • Author(s)
      T. Funaki, M. Ohnawa, Y. Suzuki, S. Yokoyama
    • Journal Title

      . Math. Anal. Appl.

      Volume: 425 Issue: 1 Pages: 20-32

    • DOI

      10.1016/j.jmaa.2014.12.018

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Front propagation for nonlinear diffusion equations on the hyperbolic space2014

    • Author(s)
      H. Matano, F. Punzo and A. Tesei
    • Journal Title

      J. Eur. Math. Soc.

      Volume: 掲載確定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Maximizing the spreading speed of KPP fronts in two-dimensional stratified media2014

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

      Proc. London Math. Soc.

      Volume: 掲載確定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity and asymptotic behavior of nonlinear Stefan problems2014

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

      Arch. Rat. Mec. Anal.

      Volume: 212 Issue: 3 Pages: 957-1010

    • DOI

      10.1007/s00205-013-0710-0

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations2014

    • Author(s)
      A. Ducrot, T. Giletti, H. Matano
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 366 Issue: 10 Pages: 5541-5566

    • DOI

      10.1090/s0002-9947-2014-06105-9

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A stable finite difference method for a Cahn-Hilliard type equation with long-range interaction2013

    • Author(s)
      Hikaru Matsuoka and Ken-Ichi Nakamura
    • Journal Title

      The Science Report of the Kanazawa University

      Volume: 57

    • NAID

      120005399934

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recurrent traveling waves in a two-dimensional saw-toothed cylinder and their average speed2013

    • Author(s)
      B. Lou, H. Matano and K.-I. Nakamura
    • Journal Title

      J. Differential Equations

      Volume: 255

    • Related Report
      2013 Annual Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the validity of formal asymptotic expansions in Allen-Cahn equationand FitzHugh-Nagumo system with generic initial data2012

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

      Discrete Contin. Dyn. Syst. Ser. B

      Volume: 17 Issue: 6 Pages: 1639-1649

    • DOI

      10.3934/dcdsb.2012.17.1639

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodically growing solutions in a class of strongly monotone semiflows2012

    • Author(s)
      K.-I.Nakamura and T,Ogiwara
    • Journal Title

      Networks and Heterogeneous Media

      Volume: Vol.7,No.4 Issue: 4 Pages: 881-891

    • DOI

      10.3934/nhm.2012.7.881

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamical structure of some nonlinear degenerate diffusion equations2012

    • Author(s)
      H. Matano and M.A. Pozio
    • Journal Title

      J. Dynamics and Differential Equations

      Volume: 24 Issue: 2 Pages: 129-149

    • DOI

      10.1007/s10884-012-9246-5

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature2012

    • Author(s)
      M. Alfaro, J. Droniou, H. Matano
    • Journal Title

      J. Evol. Equ.

      Volume: 12 Issue: 2 Pages: 267-294

    • DOI

      10.1007/s00028-011-0132-0

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A link between microscopic and macroscopic models of self-organized aggregation2012

    • Author(s)
      T. Funaki, H. Izuhara, M. Mimura and C. Urabe
    • Journal Title

      Networks and Heterogeneous Media

      Volume: 7 Issue: 4 Pages: 705-740

    • DOI

      10.3934/nhm.2012.7.705

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large time behavior of disturbed planar fronts in the Allen-Cahn equation2011

    • Author(s)
      H.Matano
    • Journal Title

      J.Differential Equations

      Volume: 251 Issue: 12 Pages: 3522-3557

    • DOI

      10.1016/j.jde.2011.08.029

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Propagation of a plant disease in some periodic medium2015

    • Author(s)
      H. Matano
    • Organizer
      GDRI-ReaDiNet workshop on "Reaction-Diffusion Sytems Arizing in Biology"
    • Place of Presentation
      ロレーヌ大学 (ナンシー,フランス)
    • Year and Date
      2015-12-17
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Front propagation in an anisotropic Allen--Cahn equation2015

    • Author(s)
      H. Matano
    • Organizer
      International Symposium on Applications of Nonlinear Partial Differential Equations in Life Science
    • Place of Presentation
      南開大学 (天津,中国)
    • Year and Date
      2015-08-04
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamics of order-preserving systems with mass consevation2015

    • Author(s)
      H. Matano
    • Organizer
      International Conference on Recent Advances in Mathematical Biology, Analysis and Applications
    • Place of Presentation
      アリガル・ムスリム大学 (アリガル,インド)
    • Year and Date
      2015-06-04
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Front propagation in a prey-predator type reaction-diffusion system2014

    • Author(s)
      H. Matano
    • Organizer
      Seoul-Tokyo Conference on "Applied Partial Differential Equations: Theory and Applications"
    • Place of Presentation
      KIAS (ソウル,韓国)
    • Year and Date
      2014-12-13
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Propagating terrace for multi-stable nonlinear diffusion equations2014

    • Author(s)
      H. Matano
    • Organizer
      Conference on Nonlinear Evolution Problems
    • Place of Presentation
      ローマ大学 (ローマ,イタリア)
    • Year and Date
      2014-06-25
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Front propagation in nonlinear diffusion equations and systems2014

    • Author(s)
      H. Matano
    • Organizer
      8th European Conference on Elliptic and Parabolic Problems
    • Place of Presentation
      ガエータ (イタリア)
    • Year and Date
      2014-05-26
    • Related Report
      2014 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Front propagation in spatially ergodic media2013

    • Author(s)
      俣野 博
    • Organizer
      UK-Japan Winter School "Nonlinear Analysis"
    • Place of Presentation
      London, UK
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Propagating terrace in 1D diffusion equations and reversed blow-up profiles in nonlinear heat equations2012

    • Author(s)
      俣野 博
    • Organizer
      9th East China PDE Conference & Shanxi International PDE Conference
    • Place of Presentation
      山西大学,中国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Reversed blow-up profile in nonlinear heat equations2012

    • Author(s)
      俣野 博
    • Organizer
      5th Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      Luminy, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Propagating terrace in one-dimensional semilinear diffusion equations2012

    • Author(s)
      俣野 博
    • Organizer
      IMA Workshop on Dynamical systems in Studies of Partial Differential Equations
    • Place of Presentation
      Univ. of Minnesota, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 3D cable model for cellular electrophysiology2012

    • Author(s)
      俣野 博
    • Organizer
      Seoul-Tokyo conference on Elliptic and Parabolic PDEs and Related Topics
    • Place of Presentation
      KIAS, Seoul, 韓国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Propagating terrace in one-dimensional semilinear diffusion equations2012

    • Author(s)
      俣野 博
    • Organizer
      Workshop on Dynamics of Patterns
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Front propagation in nonlinear diffusion equation on hyperbolic space2012

    • Author(s)
      俣野 博
    • Organizer
      International conference on Nonlinear Evolution Equations and Applications
    • Place of Presentation
      Hammamet, Tunisia
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Traveling waves in a sawtoothed cylinder and their homogenization limit2011

    • Author(s)
      俣野 博
    • Organizer
      Conference on Nonlinear Models in PDE's
    • Place of Presentation
      Toledo, Spain
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Propagating terrace in one-dimensional semilinear diffusion equation2011

    • Author(s)
      俣野 博
    • Organizer
      Conference on Fronts and nonlinear PDE's
    • Place of Presentation
      ENS, Paris, France
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Convergence results in order-preserving dynamical systems2011

    • Author(s)
      俣野 博
    • Organizer
      Conference on Asymptotic dynamics driven by solitons and traveling fronts in nonlinear PDE
    • Place of Presentation
      Univ. of Chile, Santiago, Chile
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Front propagation in spatially heterogeneous media2011

    • Author(s)
      俣野 博
    • Organizer
      第4回日本数学会季期研究所
    • Place of Presentation
      九州大学
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Traveling waves in a sawtoothed cylinder and their homogenization limit2011

    • Author(s)
      俣野 博
    • Organizer
      第55回オーストラリア数学会年会
    • Place of Presentation
      Wollongon University, Austraila
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Traveling waves in a recurrently sawtoothed cylinder and their homogenization limit2011

    • Author(s)
      俣野 博
    • Organizer
      Workshop on Stochastic Analysis on Large Scale Interacting Systems
    • Place of Presentation
      高知大学
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Dynamics of a class of systems with an order-preserving property

    • Author(s)
      H. Matano
    • Organizer
      CMC Inaugural Conference at KAIST
    • Place of Presentation
      KAIST (Daejeon, 韓国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Spreading speed for some two-component reaction-diffusion syste

    • Author(s)
      H. Matano
    • Organizer
      Journees ERC ReaDi
    • Place of Presentation
      EHESS (Paris, フランス)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] On a free boundary problem for the curvature flow with driving force

    • Author(s)
      H. Matano
    • Organizer
      LIA conference on "Mathematical Modelling and Analysis in the Life Sciences"
    • Place of Presentation
      Carry-le-Rouet (フランス)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Dynamics of fronts in multistable reaction-diffusion equations

    • Author(s)
      Ken-Ichi Nakamura
    • Organizer
      SIAM Conference on Analysis of Partial Differential Equations
    • Place of Presentation
      Orlando (米国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] KPZ equation, its renormalization and invariant measures

    • Author(s)
      T. Funaki
    • Organizer
      Stochastic Partial Differential Equations and Applications - IX
    • Place of Presentation
      台湾国立中央大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Traveling waves in an undulating cylinder

    • Author(s)
      俣野 博
    • Organizer
      Seminaire Laurent Schwartz (mini-worksho)
    • Place of Presentation
      IHES, France
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Existence and asymptotic stability of periodically growing solutions of nonlinear parabolic equations

    • Author(s)
      中村健一
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Existence of recurrent traveling waves in a two-dimensional undulating cylinder: the virtual pinning case

    • Author(s)
      中村健一
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando, USA
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Non-equilibrium fluctuations for an evolutional model of 2D Young diagrams

    • Author(s)
      舟木直久
    • Organizer
      Stochastic Partial Differential Equations and Related Topics
    • Place of Presentation
      南開大学,中国
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Presentation] Existence of recurrent traveling waves in a two-dimensional cylinder with undulating boundary - the virtual pinning case

    • Author(s)
      中村健一
    • Organizer
      Front propagation in heterogeneous media, Equadiff 2011
    • Place of Presentation
      Loughborough University, England
    • Related Report
      2011 Annual Research Report
    • Invited
  • [Funded Workshop] ICMMA 2015 `Self-Organiza-tion: Modeling and Analysis'2015

    • Place of Presentation
      明治大学(東京)
    • Year and Date
      2015-10-26
    • Related Report
      2014 Annual Research Report
  • [Funded Workshop] Singularities arising in Nonlinear Problems, SNP20142014

    • Place of Presentation
      関西セミナーハウス(京都)
    • Year and Date
      2014-11-24
    • Related Report
      2014 Annual Research Report

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Published: 2011-06-18   Modified: 2022-03-01  

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