• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Research on the structure of solutions for nonlinear systems of reaction-diffusion equations

Research Project

Project/Area Number 18540223
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, 理工学術院, 教授 (20111825)

Co-Investigator(Kenkyū-buntansha) 大谷 光春  早稲田大学, 理工学術院, 教授 (30119656)
田中 和永  早稲田大学, 理工学術院, 教授 (20188288)
久藤 衡介  福岡工業大学, 工学部, 准教授 (40386602)
若狭 徹  早稲田大学, 理工学術院, 助手 (20454069)
佐藤 典弘  早稲田大学, 理工学術院, 助手 (80454023)
中島 主恵  東京海洋大学, 海洋科学部, 助教授 (10318800)
大屋 博一  佐世保工業高等専門学校, 専任講師 (70409647)
Co-Investigator(Renkei-kenkyūsha) OTANI Mitsuharu  早稲田大学, 理工学術院, 教授 (30119656)
TANAKA Kazunaga  早稲田大学, 理工学術院, 教授 (20188288)
NAKASHIMA Kimie  東京海洋大学, 海洋科学部, 准教授 (10318800)
TAKEUCHI Shingo  工学院大学, 工学部, 准教授 (00333021)
KUTO Kousuke  福岡工業大学, 工学部, 准教授 (40386602)
OHYA Hirokazu  佐世保工業高専, 一般科目講師 (70409647)
SATO Norihiro  早稲田大学, 理工学術院, 助手 (80454023)
WAKASA Tohru  早稲田大学, 理工学術院, 助教 (20454069)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,960,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥660,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywords非線形現象 / 反応拡散方程式 / 非線形拡散 / 正値定常解 / 安定性 / 写像度理論 / 分岐理論 / Lotka-Volterra型競合モデル / 分理論 / 数理生態学
Research Abstract

数理生態学に現れる非線形拡散を伴う反応拡散方程式システムを解析した。これは生存競争を行う2種の生物種の棲み分け現象を記述するモデルとして定式化されたものである。正値定常解は2種の生物種の共存状態として生態学的にも意味のある解であり、このような解の構造解明が重要なテーマである。正値定常の存在を示すための理論・技法の開発をおこなった。同時に、非線形拡散係数を無限大とする場合の極限問題と、本来の問題との関係を調べることにより、解構造解明への手がかりをつかむことができた。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (66 results)

All 2009 2008 2007 2006 Other

All Journal Article (41 results) (of which Peer Reviewed: 31 results) Presentation (19 results) Book (4 results) Remarks (2 results)

  • [Journal Article] Global soluitions for the Shigesada-Kawasaki-Teramoto model with cross-diffusion2009

    • Author(s)
      Yoshio Yamada
    • Journal Title

      "Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions," Edited by Du, Ishii and Lin

      Pages: 282-298

    • Related Report
      2008 Final Research Report
  • [Journal Article] Bifurcation branch of stationary solutions for a Lotka-Volterra cross-diffusion system in a spatially heterogeneous environment2009

    • Author(s)
      Kousuke Kuto
    • Journal Title

      Nonlinear Anal. RWA Vol.10

      Pages: 943-965

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solutions for the Shigesada-Kawasaki-Teramoto model with cross-diffusion2009

    • Author(s)
      Yoshio Yamada
    • Journal Title

      Reaction-Diffusion Systems and Viscosity Solutions

      Pages: 282-299

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type2009

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

      Differential and Integral Equations (出版確定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Positive solutions for Lotka-Volterra systems with cross- diffusion2008

    • Author(s)
      Yoshio Yamada
    • Journal Title

      "Handbook of Differential Equations : Stationary Partial Differential Equations," Edited by M.Chipot Vol.6

      Pages: 411-501

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability from the point of view of diffusion, relaxation and spatial inhomogeneity2008

    • Author(s)
      Fang Li, Kimie Nakashima and Wei-Ming Ni
    • Journal Title

      Discrete Contin. Dyn. Syst Vol.20

      Pages: 259-274

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of global solutions for a semilinear parabolic Cauchy problem2008

    • Author(s)
      Munemitsu Hirose
    • Journal Title

      Differential Integral Equations Vol.21

      Pages: 623-652

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] 回転する障害物の周りでの非圧縮性粘性流体の方程式の数学解析2008

    • Author(s)
      菱田俊明
    • Journal Title

      数学 第60巻

      Pages: 68-94

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Highly oscillatory behavior of the activator in the Gierer and Meinhardt system2008

    • Author(s)
      P. Felmer, S. Martinez and Kazunaga Tanaka
    • Journal Title

      Math. Ann Vol.340

      Pages: 749-773

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Positive solutions for Lotka-Volterra ystems with cross-diffusion2008

    • Author(s)
      Yoshio Yamada
    • Journal Title

      Handbook of Differential Equations : stationary Partial Differential Equations 6

      Pages: 411-511

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Highly oscillatory behavior of the activator in the Gierer and Meinhardt system2008

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

      Mathematische Annalen 340巻

      Pages: 749-773

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Sability from the point of view Of diffusion,relaxation and spatial inhomogeneity2008

    • Author(s)
      Fang Li, Kimie Makashima and Wei-MingNi
    • Journal Title

      Discrete and Continuous Dynamical Systems 20巻

      Pages: 259-274

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Infinite dimensional attractors for evolution equations with p-Laplacian and their Kolmogorov entropy2007

    • Author(s)
      M. A. Efendiev and Mitsuharu Otani
    • Journal Title

      Differential Integral Equations Vol.20

      Pages: 1201-1209

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Morse index of layered solutions to the heterogeneous Allen-Cahn equation2007

    • Author(s)
      Yihong Du and Kimie Nakashima
    • Journal Title

      J. Differential Equations Vol.238

      Pages: 87-117

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generation of interfaces for Lotka-Volterra competition-diffusion system with large interaction rates2007

    • Author(s)
      Kimie Nakashima and Tohru Wakasa
    • Journal Title

      J. Differential Equations Vol.235

      Pages: 586-608

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A strongly coupled diffusion effect on the stationary set of a prey-predator model2007

    • Author(s)
      Kousuke Kuto
    • Journal Title

      Adv. Differential Equations Vol.12

      Pages: 145-172

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Coincidence sets in semilinear elliptic problems of logistic type2007

    • Author(s)
      Shingo Takeuchi
    • Journal Title

      Differential Integral Equations Vol.20

      Pages: 1075-1080

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infinite-dimentional attractors for evolution equations with p-Laplacian and their Kolmogorov entropy2007

    • Author(s)
      Messoud A.Efendiev and Mitsuharu Otani
    • Journal Title

      Differential Integral Eauations 20巻

      Pages: 1201-1209

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence of nontrivial solutions for some elliptic equations with supercritical nonlinearity in exterior domains2007

    • Author(s)
      Satoshi Hashimoto and Mitsuharu otani
    • Journal Title

      Discrete and Continuous Dynamical Systems 19巻

      Pages: 323-333

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stationary Navier-Stokes flow around a rotating obstacle2007

    • Author(s)
      Reinhardt Farwig and Toshiaki Hishida
    • Journal Title

      Funkcialaj Ekvacioj 50巻

      Pages: 371-403

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Steady motions of the Navier-Stokes fluid around a rotating body2007

    • Author(s)
      Toshiaki Hishida
    • Journal Title

      Advanced Studies in Pure Mathematics 47巻

      Pages: 117-136

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness of positive solutions to scalar field equations with harmonic potential2007

    • Author(s)
      Munemitsu Hirose and Masahito Ohta
    • Journal Title

      Funkcialaj Ekvaioj 50巻

      Pages: 67-100

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generation of interfaces for Lotka-Volterra competition-diffusion system with large interaction rates2007

    • Author(s)
      Kimie Nakashima and Tohru Wakasa
    • Journal Title

      Journal of Differential Equations 235巻

      Pages: 586-608

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Morse index of layered solutions to the heterogeneous Allen-Cahn equation2007

    • Author(s)
      Yihong Du and Kimie Nakashima
    • Journal Title

      Journal of Differential Equations 238巻

      Pages: 87-117

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singular limit of a spatially inhomogeneous Lotka-Volterra cometition-diffusion system2007

    • Author(s)
      D.Hilhorst, G.Karali, H.Matano and K.Nakashima
    • Journal Title

      Communications in Partial Differential Equations 32巻

      Pages: 879-933

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Coincidence sets in semilinear elliptic problems of logistic type2007

    • Author(s)
      Shingo Takeuchi
    • Journal Title

      Differential Integral Equations 20巻

      Pages: 1075-1080

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A strongly coupled diffusion effect on the stationary solution set of a prey-predator model2007

    • Author(s)
      Kousuke Kuto
    • Journal Title

      Advances in Differential Equations 12巻

      Pages: 145-172

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generation of interfaces for Lotka-Volterra competition-diffusion system with large interaction rates2007

    • Author(s)
      K.Nakashima, T.Wakasa
    • Journal Title

      Journal of Differential Equations Vol.235,NO.2

      Pages: 586-608

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Positive steady states for a prey-predator model with some nonlinear diffusion terms2006

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

      J. Math. Anal. Appl Vol.323

      Pages: 1387-1401

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exact eigenvalues and eigenfunctions associated with linearization for Chafee-Infante problem2006

    • Author(s)
      Wakasa Tohru
    • Journal Title

      Funkcial. Ekvac Vol.49

      Pages: 321-336

    • NAID

      130000140670

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiple stable patterns for some reaction-diffusion equation in disrupted environments2006

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

      Discrete Contin. Dyn. Syst Vol.14

      Pages: 93-116

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Steady-states with transition layers and spik es for a bistable reaction-diffusion eauation2006

    • Author(s)
      M.Urano, K.Nakashima, Y.Yamada
    • Journal Title

      Mathematical Approach to Nonlinear Phenomena : Modelling,Analysis and Simulations, GAKUTO Internat.Ser.Math. Sci.Appl. Vol.23

      Pages: 267-279

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Convergence of periodic systems governed by subdifferential operators2006

    • Author(s)
      M.Otani
    • Journal Title

      Mathematical Approach to Nonlinear Phenomena : Modelling,Analysis and Simulations, GAKUTO Internat.Ser.Math. Sci.Appl. Vol.23

      Pages: 217-228

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The fixed energy problem for a class of nonconvex singular Hamiltonian system2006

    • Author(s)
      C.Carminati, E.Sere, K.Tanaka
    • Journal Title

      Journal of Differential Eauations Vol.230,No.1

      Pages: 362-377

    • Related Report
      2006 Annual Research Report
  • [Journal Article] High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrodinger equation2006

    • Author(s)
      P.Felmer, S.Martinez, K.Tanaka
    • Journal Title

      Archive for Rational Mechanics and Analysis Vol.182,No.2

      Pages: 333-366

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the number of positive solutions of singularly perturbed 1D nonlinear Schrodinger equations2006

    • Author(s)
      P.Felmer, S.Martinez, K.Tanaka
    • Journal Title

      Journal of the European Mathematical Society Vol.8,No.2

      Pages: 253-268

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Positive steady states for aprey-predator model with some nonlinear diffusion terms2006

    • Author(s)
      T.Kadota, K.Kuto
    • Journal Title

      Journal of Mathematicl Analysis and Applications Vol.323,No.2

      Pages: 1387-1401

    • Related Report
      2006 Annual Research Report
  • [Journal Article] L^q estimates of weak solutions to the stationary Stokes equations around a rotating body2006

    • Author(s)
      T.Hishida
    • Journal Title

      Journal of the Mathematical Society of Japan Vol.58,No.3

      Pages: 743-767

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type

    • Author(s)
      KousukeKuto and Yoshio Yamada
    • Journal Title

      Differential Integral Equations (発表予定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Positive solutions for Lotka-Volterra systems with cross-diffusin

    • Author(s)
      Yoshio Yamada
    • Journal Title

      Handbook of Differential Equations:Stationary Partial Differential Equatlons 第6巻(印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representation formulas for some 1-dimensionallinearized eigenvalue probiems

    • Author(s)
      shoji Yotsutani and Tohru Wakasa
    • Journal Title

      Communications in Pure and Applied Analysis (印刷中)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Bifurcation structure of steady-states for an adsorbate-induced phase transition model2008

    • Author(s)
      久藤衡介
    • Organizer
      「非線形発展方程式と現象の数理モデル」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2008-11-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Limiting charaoetrization for coexistenoe states for a Lotka-Volterra model with nonlinear diffusion of fractional type2008

    • Author(s)
      久藤衡介, 山田義雄
    • Organizer
      日本数学会秋季学会
    • Place of Presentation
      東工大
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Limiting characterization for coexistence states to a Lotka-Volterra model with nonlinear diffusion of fractional type2008

    • Author(s)
      久藤衡介、山田義雄
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東工大
    • Year and Date
      2008-09-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Limiting behavior of solutions for some reaction-diffusion systems with nonlinear diffusion2008

    • Author(s)
      Yoshio Yamada
    • Organizer
      The 5^<th> World Congress of Nonlinear Analysts
    • Place of Presentation
      Orlando, Florida, USA
    • Year and Date
      2008-07-03
    • Related Report
      2008 Final Research Report
  • [Presentation] Coexistence problem for a prey-predator model with density- dependent diffusion2008

    • Author(s)
      Kousuke Kuto
    • Organizer
      The 5^<th> World Congress of Nonlinear Analysts
    • Place of Presentation
      Orlando, Florida, USA
    • Year and Date
      2008-07-03
    • Related Report
      2008 Final Research Report
  • [Presentation] Limiting behavior of solutions for some reaction-diffusion systems with nonlinear diffusion2008

    • Author(s)
      Yoshio Yamada
    • Organizer
      5th World Congress of Nonlinear Analysts
    • Place of Presentation
      フロリダ州オーランド
    • Year and Date
      2008-07-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] 回転する障害物の周りでの非圧縮粘性流体の方程式の数学解析2008

    • Author(s)
      菱田 俊明
    • Organizer
      日本数学会 2007年度解析学賞受賞特別講演
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] ある線形化固有値問題の全ての固有値と固有関数につえい2008

    • Author(s)
      若狭 徹
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Limiting characterization of stationary solutions for some Lotka-Volterra models with nonlinear diffusion2007

    • Author(s)
      Yoshio Yamada
    • Organizer
      Workshop on Recent Advances on Nonlinear Parabolic and Elliptic Differential Equations
    • Place of Presentation
      龍谷大学
    • Year and Date
      2007-12-04
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] ある反応拡散方程式に対するCauchy問題の大域解の存在について2007

    • Author(s)
      廣瀬 宗光
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] ある反応拡散方程式システムに関する定常問題について2007

    • Author(s)
      佐藤 典弘
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the relation between the large time behavior of the Stokes semigroup and the decay of steady Stokes flow at infinity2007

    • Author(s)
      菱田 俊明
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Representation and asymptotic formulas for some 1-imensional linearized eigenvalue problems2007

    • Author(s)
      若狭 徹
    • Organizer
      RIMS研究集会「変分問題とその周辺」
    • Place of Presentation
      京都大学数理研
    • Year and Date
      2007-06-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] Population models of interacting species with cross and self diffusion2007

    • Author(s)
      Yoshio Yamada
    • Organizer
      Eco Summit 2007
    • Place of Presentation
      北京九貨山庄(Jiuhua Resort & Convention Center)
    • Year and Date
      2007-05-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Population models of interacting species with cross and self diffusion2007

    • Author(s)
      Yoshio Yamada
    • Organizer
      EcoSummit 2007
    • Place of Presentation
      北京
    • Year and Date
      2007-05-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Stability of steady-states to the SKT model in a heterogeneous environment2007

    • Author(s)
      久藤衡介
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] 数理生態学におけるSKTモデルと関連する話題2006

    • Author(s)
      山田義雄
    • Organizer
      東北大学数学教室談話会
    • Place of Presentation
      東北大学
    • Year and Date
      2006-11-06
    • Related Report
      2008 Final Research Report
  • [Presentation] A Lotka-Volterra cross- diffusion model in spatially hetero- geneous environments2006

    • Author(s)
      久藤衡介
    • Organizer
      現象の数理モデルと発展方程式」研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2008 Final Research Report
  • [Presentation] 空間非一様な環境下でのLotka-Volterra拡散系に対する定常解2006

    • Author(s)
      久藤衡介
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪府立大学
    • Related Report
      2008 Final Research Report
  • [Book] 理工系のための微分積分I, II2007

    • Author(s)
      鈴木武、山田義雄、柴田良弘、田中和永
    • Total Pages
      478
    • Publisher
      内田老鶴圃
    • Related Report
      2008 Final Research Report
  • [Book] 理工系のための「微分積分I, II」2007

    • Author(s)
      鈴木 武、山田 義雄、柴田 良弘、田中 和永
    • Total Pages
      478
    • Publisher
      内田老鶴圃
    • Related Report
      2007 Annual Research Report
  • [Book] 理工系のための「微分積分問題と解説I, II」2007

    • Author(s)
      鈴木 武、山田 義雄、柴田 良弘、田中 和永
    • Total Pages
      187
    • Publisher
      内田老鶴圃
    • Related Report
      2007 Annual Research Report
  • [Book] 理工系のための「微分積分」2007

    • Author(s)
      鈴木 武, 山田 義雄, 柴田 良弘, 田中 和永
    • Total Pages
      240
    • Publisher
      内田老鶴圃
    • Related Report
      2006 Annual Research Report
  • [Remarks]

    • URL

      http://www.f.waseda.jp/yamada/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.f.waseda.jp/yamada/

    • Related Report
      2008 Annual Research Report

URL: 

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

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi