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Research of System of Nonlinear Diffusion Equations and Related Elliptic Differential Equations

Research Project

Project/Area Number 15540216
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionWaseda University

Principal Investigator

YAMADA Yoshio  Waseda University, Faculty of Science and Engineering, Professor, 理工学術院, 教授 (20111825)

Co-Investigator(Kenkyū-buntansha) OTANI Mitsuharu  Waseda University, Faculty of Science and Engineering, Professor, 理工学術院, 教授 (30119656)
TANAKA Kazunaga  Waseda University, Faculty of Science and Engineering, Professor, 理工学術院, 教授 (20188288)
NAKASHIMA Kimie  Tokyo University of Marine Science and Technology, Faculty of Marine Science, Associate Professor, 海洋科学部, 助教授 (10318800)
TAKEUCHI Shingo  Kogakuin University, Faculty of Engineering, Lecturer, 工学部, 講師 (00333021)
KUTO Kousuke  Fukuoka Institute of Technology, Faculty of Engineering, Lecturer, 工学部, 講師 (40386602)
菱田 俊明  新潟大学, 工学部, 助教授 (60257243)
Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsreaction-diffusion / quasilinear diffusion / internal transition layer / spike / steady-state solution / stability / prey-predator model / Morse index / 正値定常解 / prey-predator
Research Abstract

In this project, we have studied the structure of solutions for the following two types of equations : (a) reaction diffusion systems with nonlinear diffusion in mathematical biology and (b) semilinear diffusion equations describing phase transition phenomena
The first problem in mathematical biology is given by a system of differential equations with quasilinear diffusion of the form
u_t=Δ[φ(u,v)u]+au(1-u-v), v_t=Δ[ψ(u,v)v]+bv(1+du-v),
under homogeneous Dirichlet boundary conditions. Here u and v denote population densities of prey and predator species, respectively. It is well known that the corresponding stationary problem has a positive steady-state under a suitable condition. Our main interest is to derive useful information on profile and stability of each positive steady-state. In case φ(u,v)=1 and 4,φ(u,v=1+β u, we have shown that the stationary problem has at least three positive solutions if β is sufficiently large and some other conditions are imposed. Moreover, stability or in … More stability of each positive solution is also investigated.
The second problem is given by u_t=ε^2u_<xx>+u(1-u)(u-a(x)) with homogeneous Neumann boundary condition, where 0<a(x)<1. When ε is sufficiently small, it is known that this problem admits various kinds of steady-state solutions. In particular, we are interested in steady state with transition layers and spikes. Here transition layer for a solution means a part of u(x) where u(x) drastically changes from 0 to 1 or 1 to 0 in a very short interval. Such oscillating solutions have been studied by Ai-Chen-Hastings and our group, independently. It has been proved that any transition layer appears only in a neighborhood of x such that a(x)=1/2 and that any spike appears only in a neighborhood of x such that a(x) takes its local maximum or minimum. We have also established more information on profiles of multi-transition layers and multi-spikes, their location and the relationship between profile and stability of steady-state solution with transition layers. Less

Report

(4 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (66 results)

All 2006 2005 2004 2003 Other

All Journal Article (55 results) Publications (11 results)

  • [Journal Article] Positive steady states for a prey-predator model with some nonlinear diffusion terms2006

    • Author(s)
      門田智仁, 久藤衡介
    • Journal Title

      Journal of Mathematical Analysis and Applications (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multiple stable patterns for some reaction-diffusion equation in disrupted environments2006

    • Author(s)
      倉田和浩, 田中和永 他1名
    • Journal Title

      Discrete`and Continuous Dynamical Systems 14巻1号

      Pages: 93-116

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Positive steady states for a prey-prdator model with some nonlinear diffusion terms2006

    • Author(s)
      Tomohito Kadota, Kousuke Kuto
    • Journal Title

      Journal of Mathematical Analysis and Applications (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multiple stable patterns for some reaction-diffusion equation in disrupted environments2006

    • Author(s)
      Takanori Ide, Kazuhiro Kurata, Kazunaga Tanaka
    • Journal Title

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

      Pages: 93-116

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Positive steady states for a prey-predator model with some nonlinear diffusion terms2006

    • Author(s)
      Tomohito Kadota, kousuke Kuto
    • Journal Title

      Jouranl of Matheamtical Analysis and Applications (印刷中)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Transition layers and spikes for a bistable reaction-diffusion equation.2005

    • Author(s)
      浦野道雄, 中島主恵, 山田義雄
    • Journal Title

      Advances in Mathematical Sciences and Applications 15巻2号

      Pages: 683-707

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Coexistence states for a prey-predator model with cross-diffusion2005

    • Author(s)
      久藤 衡介, 山田義雄
    • Journal Title

      Dynamical Systems and Differential Equations

      Pages: 536-545

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition layers and spikes for a reaction-diffusion equation with bistable nonlinearity2005

    • Author(s)
      浦野道雄, 中島主恵, 山田義雄
    • Journal Title

      Dynamical Systems and Differential Equations

      Pages: 868-877

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Local well posedness of the Cauchy problem for the Landau-Lifshitz equations2005

    • Author(s)
      Atsushi Fuwa, 堤正義
    • Journal Title

      Differential and Integral Equations 18巻4号

      Pages: 379-404

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces2005

    • Author(s)
      赤木剛朗, 大谷光春
    • Journal Title

      Journal of Differential Equations 209巻2号

      Pages: 392-415

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A positive solution for a nonlinear Schrodinger equation on R^{N}2005

    • Author(s)
      Louis Jeanjean, 田中和永
    • Journal Title

      Indiana University Mathematics journal 54巻2号

      Pages: 443-464

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multi-clustered high energy solutions for a phase transition problem2005

    • Author(s)
      Patricio L.Felmer, Salome-Martinez, 田中和永
    • Journal Title

      Proceedings of the Royal Society of Edinburgh, Sect. A 135巻4号

      Pages: 731-765

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition layers and spikes for a bistable reaction- diffusion equation2005

    • Author(s)
      Michio Urano, Kimie Nakashima, Yoshio Yamada
    • Journal Title

      Advances in Mathematical Sciences and Applications Vol.15, No.2

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Coexistence states for a prey-predator model with cross-diffusion2005

    • Author(s)
      Kousuke Kuto, Yoshio Yamada
    • Journal Title

      Dynamical Systems and Differential Equations

      Pages: 536-545

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Transition layers and spikes for a reaction- diffusion equation with bistable nonlinearity2005

    • Author(s)
      Michio Urano, Kimie Nakashima, Yoshio Yamada
    • Journal Title

      Dynamical Systems and Differential Equations

      Pages: 868-877

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Local well posedness of the Cauchy problem for the Landau-Lifshitz equations2005

    • Author(s)
      Atsushi Fuwa, Masayoshi Tsutsumi
    • Journal Title

      Differential and Integral Equations Vol.18, No.4

      Pages: 379-404

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces2005

    • Author(s)
      Goro Akagi, Mitsuharu Otani
    • Journal Title

      Journal of Differential Equations Vol.209, No.2

      Pages: 392-415

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] A positive solution for a nonlinear Schrodinger equation in RAINY^{N}2005

    • Author(s)
      Louis Jeanjean, Kazunaga Tanaka
    • Journal Title

      Indiana University Mathematics Journal Vol.54, No.2

      Pages: 443-464

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multi-clustered high energy solutions for a phase transition problem2005

    • Author(s)
      Patricio L.Felmer, Salome Martinez, Kazunaga Tanaka
    • Journal Title

      Proceedings of the Royal Society of Edinburgh, Sect A Vol.135, No.4

      Pages: 731-765

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Transition layers and spikes for a bistable reaction- diffusion equation2005

    • Author(s)
      Micio Urano, Kimie Nakashima, Yoshio Yamada
    • Journal Title

      Advances in Mathematical Sciences and Applications Vol.15, No.2

      Pages: 683-707

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Evolution inclusions governed by the difference of two subdifferentials in reflexive Banach spaces2005

    • Author(s)
      Goro Akagi, Mitsuharu Otani
    • Journal Title

      Journal of Differential Equations Vol.209

      Pages: 392-415

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A positive solution for a nonlinear Schroedinger equation in R^{N}2005

    • Author(s)
      Louis Jeanjean, Kazunaga Tanaka
    • Journal Title

      Indiana Univeristy Mathematics Journal Vol.54, No.2

      Pages: 443-464

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Multi-clustered high-energy solutions for a phase transition problem2005

    • Author(s)
      Patricio Felmer, Salome Martinez, Kazunaga Tanaka
    • Journal Title

      Proceedings of the Royal Society of Edinburgh, Sect.A Vol.135, No.4

      Pages: 731-765

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Coexistence states for a prey-predator model with cross diffusion2005

    • Author(s)
      Kousuke Kuto, Yoshio Yamada
    • Journal Title

      Proceedings of AIMS' 5th International Conference on Dynamical Systems and Differential Equaitons, June 2004, Pomona, CA (予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Transition layers and spikes for a reaction-diffusion equation with bistable nonlinearity2005

    • Author(s)
      Michio Urano, Kimie Nakashima, Yoshio Yamada
    • Journal Title

      Proceedings of AIMS' 5th Internatonal Conference on Dynamical Systems and Differential Equations, June 2004, Pomona, CA (予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Multiple coexistence states for a prey-predator system with cross-diffusion2004

    • Author(s)
      久藤 衡介, 山由義雄
    • Journal Title

      Journal of Differential Equations 197巻2号

      Pages: 315-348

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion2004

    • Author(s)
      Y.S.Choi, Roger Lui, 山田義雄
    • Journal Title

      Discrete and Continuous Dynamical Systems 10巻3号

      Pages: 719-730

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Degree for subdifferential operators in Hilbert spaces2004

    • Author(s)
      小林純, 大谷光春
    • Journal Title

      Advances in Mathematical. Sciences and Applications 14巻1号

      Pages: 307-325

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The Landau-Lifshitz flow of maps into the Lobachevsky plane2004

    • Author(s)
      堤 正義
    • Journal Title

      Funkcialaj Ekvacioj 47巻1号

      Pages: 83-106

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities2004

    • Author(s)
      Louis Jeanjean, 田中和永
    • Journal Title

      Calculus of Variations and Partial Differential Equations 21巻3号

      Pages: 287-318

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stability of steady-state solutions to a prey-predator system with cross-diffusion2004

    • Author(s)
      久藤 衡介
    • Journal Title

      Journal of Differential Equations 197巻2号

      Pages: 293-314

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multiple coexistence states for a prey-predator system with cross-diffusion2004

    • Author(s)
      Kousuke Kuto, Yoshio Yamada
    • Journal Title

      Journal of Differential Equations Vol.197, No.2

      Pages: 315-348

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Existence of global solutions for the Shiesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion2004

    • Author(s)
      Y.S.Choi, Roger Lui, Yoshio Yamada
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.10, No.3

      Pages: 719-730

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Degree for subduifferential operators in Hilbert spaces2004

    • Author(s)
      Jun Kobayashi, Mitsuharu Otani
    • Journal Title

      Advances in Mathematical Sciences and Applications Vol.14, No.1

      Pages: 307-325

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] The Landau-Lifshitz flow of maps into the Lobachevsky plane2004

    • Author(s)
      Masayoshi Tsutsumi
    • Journal Title

      Funkcialaj Ekvacioj vole.47, No.1

      Pages: 83-106

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities2004

    • Author(s)
      Louis Jeanjean, Kazunaga Tanaka
    • Journal Title

      Calculus of Variations and Partial Differential Equations Vol.21, No.3

      Pages: 287-318

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] Stability of steady-state solutions to a prey-predator system with cross-diffusion2004

    • Author(s)
      Kousuke Kuto
    • Journal Title

      Journal of Differential Equations Vol.197, No.2

      Pages: 293-314

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion2004

    • Author(s)
      Kousuke Kuto, Yoshio Yamada
    • Journal Title

      Nonlocal Elliptic and Parabolic Problems, Banach Center Publications 66

      Pages: 199-210

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Landau-Lifschitz flow of maps into the Lobachevsky plane2004

    • Author(s)
      Masayoshi Tsutsumi
    • Journal Title

      Funkcialaj Ekvacioj Vol.47, No.1

      Pages: 83-106

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Degree for subdifferential operators in Hilbert spaces2004

    • Author(s)
      Jun Kobayashi, Mitsuharu Otani
    • Journal Title

      Advances in Mathematical Sciences and Applications Vol.14, No.1

      Pages: 307-325

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Topological degree for S_{+}-mappings with maximal monotone perturbations and its applications to variational inequalities2004

    • Author(s)
      Jun Kobayashi, Mitsuharu Otani
    • Journal Title

      Nonlinear Analysis Vol.59, No.1-2

      Pages: 147-172

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Evolution inclusions governed by subdifferentials in reflexive Banach spaces2004

    • Author(s)
      Goro Akagi, Mitsuharu Otani
    • Journal Title

      Journal of Evolution Equations Vol.4, No.4

      Pages: 519-541

    • Related Report
      2004 Annual Research Report
  • [Journal Article] L^{q}-theory of a singular "winding" integral operator arising from fluid dynamics2004

    • Author(s)
      Reinhard Farwig, Toshiaki Hishida, Detlef Muller
    • Journal Title

      Pacific Journal of Mathematics Vol.215, No.2

      Pages: 297-312

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion2003

    • Author(s)
      Y.S.Choi, Roger Lui, 山田義雄
    • Journal Title

      Discrete and Continuous Dynamical Systems 9巻5号

      Pages: 1193-1200

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Principle of symmetric criticality and evolution equations2003

    • Author(s)
      赤木剛朗, 小林純, 大谷光春
    • Journal Title

      Dynamical Systems and Differential Equations

      Pages: 1-10

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multiplicity of positive solutions of a nonlinear Schrodinger equation2003

    • Author(s)
      Yanheng Ding, 田中和永
    • Journal Title

      Manuscripta Mathematica 112巻1号

      Pages: 109-135

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multi-layered stationary solutions for a spatially inhomogeneous Allen-Cahn equation2003

    • Author(s)
      中島主恵
    • Journal Title

      Journal of Differential Equations 191巻1号

      Pages: 234-276

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Clustering layers and boundary layers in spatially inhomogeneous phase transition problems2003

    • Author(s)
      中島主恵, 田中和永
    • Journal Title

      Annes de l'Institut Henri Poincare, Analyse Non Lineaire 20巻1号

      Pages: 107-143

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Global attractor for a class of degenerate diffusion equations2003

    • Author(s)
      竹内慎吾, 横田智巳
    • Journal Title

      Electron Journal of Differential Equations 2003,76号

      Pages: 1-13

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Existence of global solutions for the Shiesada-Kawasaki-Teramoto model with weak cross-diffusion2003

    • Author(s)
      Y.S.Choi, Roger Lui, Yoshio Yamada
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.9, No.5

      Pages: 1193-1200

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Principle of symmetric criticality, evolution equations2003

    • Author(s)
      Goro Akagi, Jun Kobayashi, Mitsuharu Otani
    • Journal Title

      Dynamical Systems and Differential Equations

      Pages: 1-10

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multiplicity of positive solutions of a nonlinear Schrodinger equation2003

    • Author(s)
      Yanheng Ding, Kazunaga Tanaka
    • Journal Title

      Manuscripta Mathematica Vol.112, No.1

      Pages: 109-135

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Multi-layered stationary solutions for a spatially in homogeneous Allen-Cahn equation2003

    • Author(s)
      Kimie Nakashima
    • Journal Title

      Journal of Differential Equations Vol.191, No.1

      Pages: 234-276

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Clustering layers and boundary layers in spatially inhomogeneous phase transition problems2003

    • Author(s)
      Kimie Nakashima, Kazunaga Tanaka
    • Journal Title

      Annales de l'Institute Henri Poincare, Analyse Non Lineaire Vol.20, No.1

      Pages: 107-143

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Global attractors for a class of degenerate diffusion equations2003

    • Author(s)
      Shingo Takeuchi, Tomomi Yokota
    • Journal Title

      Electron Journal of Differential Equations No.76

      Pages: 1-13

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] Kousuke Kuto, Yoshio Yamada: "Multiple coexistence states a prey-predator with cross-diffusion"J.Differential Equations. Vol.197. 315-348 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.S.Choi, Roger Lui, Yoshio Yamada: "Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion"Discrete and Continuous Dynamical Systems. Vol.10,No.4. 719-730 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.S.Choi, Roger Lui, Yoshio Yamada: "Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion"Discrete and Continuous Dynamical Systems. Vol.9,No.5. 1193-1200 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Goro Akagi, Mitsuharu Otani: "Evolution equations and subdifferentials in Banach spaces"Dynamical Systems and Differential Equations. 11-20 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Goro Akagi, Jun Kobayashi, Mitsuharu Otani: "Principle of symmetric criticality and evolution equations"Dynamical Systems and Differential Equations. 1-10 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Lui Jeanjean, Kazunaga Tanaka: "A note on mountain pass characterization of least energy solutions"Adv.Nonlinear Stud.. Vol.3,No.4. 445-455 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Yanheng Ding, Kazunaga Tanaka: "Multiplicity of positive solutions of a nonlinear Schrodinger equation"Manuscripta Math.. Vol.112,No.1. 109-135 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Toshiaki Hishida: "The nonstationary Stokes and Navier-Stokes flows through an aperture"Adv.Math.Fluid Mech.. Vol.3(印刷中). (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kimie Nakashima: "Multi-layered stationary solutions for a stationary inhomogeneous Allen Cahn equation"J.Differential Equations. Vol.191,No.1. 234-276 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Kimie Nakashina, Kazunaga Tanaka: "Clustering layers and boundary layers in spatially inhomogeneous phase transition problems"Ann.Inst.H.Poincare Anal. Non Lineaire. Vol.20,No.1. 107-143 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Shingo Takeuchi, Tomomi Yokota: "Global attactors for a class of degenerate diffusion equation"Electron.J.Differential Equations. no.76(electronic). 13 (2003)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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