Study on spatial pattern solutions for the Lotka-Volterra system with advection

• Project/Area Number: 21740129
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: The University of Electro-Communications (2010-2011); Fukuoka Institute of Technology (2009)
• Principal Investigator: KUTO Kousuke 電気通信大学, 情報理工学研究科, 准教授 (40386602)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 非線形数理 / 反応拡散移流系 / 定常解 / 分岐 / 数理生物モデル / 極限系 / 移流 / 反応拡散 / 楕円型偏微分方程式 / 境界条件 / 現象の数理 / ロトカ・ボルテラ系 / 反応拡散系 / 定常パターン / 数理モデル / 相互拡散 / アプリオリ評価 / 漸近解析 / 写像度

Research Abstract

We derive some mathematical information on the global bifurcation structure of stationary solutions to the Lotka-Volterra system with nonlinear diffusion. First we study the Lotka-Volterra competition system with cross-diffusion under the Dirichlet boundary conditions to obtain the global bifurcation branch of a subset of stationary solutions to the limiting system as a cross-diffusion term tends to infinity. We also study a reaction-diffusion-advection system related to the Lotka-Volterra system and obtain the global bifurcation structure of stationary solutions to the limiting system as the diffusion and advection terms tend to infinity.

Research Products

• [Journal Article] Univesal bound for stationary patterns of an adsorbate-induced phase transitionmodel (2011)
  • Author(s): Kousuke Kuto, Tohru Tsujikawa
  • Journal Title: Journal of Math-for-Industry Volume: 3-C-9 Pages: 69-72
  • URL: https://qir.kyushu-u.ac.jp/dspace/handle/2324/20614
  • Peer Reviewed
• [Journal Article] Universal bound for stationary patterns of an adsorbate-induced phase transition model (2011)
  • Author(s): Kousuke Kuto, Tohru Tsujikawa
  • Journal Title: Journal of Math-for-Industry Volume: 3(C) Pages: 69-72
  • Peer Reviewed
• [Journal Article] Stationary patterns for an adsorbateinducedphase transition model I (2010)
  • Author(s): Kousuke Kuto, Tohru Tsujikawa
  • Journal Title: Discrete and Continuous Dynamical Systems-Series B Volume: 14-3 Issue: 3 Pages: 1105-1117
  • DOI: 10.3934/dcdsb.2010.14.1105
  • Peer Reviewed
• [Journal Article] Positivesolutions for Lotka-Volterra competitionsystems with large cross-diffusion (2010)
  • Author(s): Kousuke Kuto, Yoshio Yamada
  • Journal Title: Applicable Analysis Volume: 89-7 Issue: 7 Pages: 1037-1066
  • DOI: 10.1080/00036811003627534
  • Peer Reviewed
• [Journal Article] Positive solutions for Lotka-Volterra competition systems with large cross-diffusion (2010)
  • Author(s): Kousuke Kuto, Yoshio Yamada
  • Journal Title: Applicable Analysis Volume: 89 Pages: 1037-1066
  • Peer Reviewed
• [Journal Article] Stationary patterns for an adsorbate-induced phase transition model I : Existence (2010)
  • Author(s): Kousuke Kuto, Tohru Tsujikawa
  • Journal Title: Discrete and Continuous Dynamical Systems-Series B Volume: 14 Pages: 1105-1117
  • Peer Reviewed
• [Journal Article] Bifurcation branch of stationary solutions for a Lotka-Volterra cross-diffusion system in a spatially heterogeneous environment (2009)
  • Author(s): Kousuke Kuto
  • Journal Title: Nonlinear Analysis Series B, Real World Applications 10 Pages: 943-965
  • Peer Reviewed
• [Journal Article] Stability and Hopf bifurcation of coexistence steady-states to an SKT Model in a spatially heterogeneous environment (2009)
  • Author(s): Kousuke Kuto
  • Journal Title: Discrete and Continuous Dynamical Systems 24 Pages: 489-509
  • Peer Reviewed
• [Journal Article] Coexistence problem for a prey-predator model with density-dependent diffusion (2009)
  • Author(s): Kousuke Kuto, Yoshio Yamada
  • Journal Title: Nonlinear Analysis : Theory, Methods & Applications 71
  • Peer Reviewed
• [Journal Article] Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type (2009)
  • Author(s): Kousuke Kuto, Yoshio Yamada
  • Journal Title: Differential and Integral Equations 22 Pages: 725-752
  • Peer Reviewed
• [Journal Article] Shadow system for adsorbate-induced phase transition model (2009)
  • Author(s): Kousuke Kuto, Tohru Tsujikawa
  • Journal Title: 数理解析研究所講究録 別冊15 Pages: 1-14
  • Peer Reviewed
• [Journal Article] Bifurcation structure of steady states for an adsorbate-induced phase transition model (2009)
  • Author(s): Kousuke Kuto
  • Journal Title: 数理解析研究所講究録 1640 Pages: 129-143
• [Presentation] Stationary problem for areaction-diffusion-advection system insurface chemistry (2011)
  • Author(s): 久藤衡介
  • Organizer: 日本数学会函数方程式論分科会研究集会
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-12-18
• [Presentation] Stationary problem for a reaction-diffusion-advection system in surface chemistry (2011)
  • Author(s): 久藤衡介
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-12-18
• [Presentation] Coexistence statesfor the SKT model with large crossdiffusion (2011)
  • Author(s): 久藤衡介,山田義雄
  • Organizer: 日本数学会総合分科会函数方程式論分科会
  • Place of Presentation: 信州大学松本キャンパス
  • Year and Date: 2011-09-28
• [Presentation] Bifurcation structureof stationary layers for an adsorbate induced phase transition model (2011)
  • Author(s): 久藤衡介,辻川亨
  • Organizer: 日本数学会総合分科会函数方程式論分科会
  • Place of Presentation: 信州大学松本キャンパス
  • Year and Date: 2011-09-28
• [Presentation] Coexistence states for the SKT model with large cross-diffusion (2011)
  • Author(s): 久藤衡介、山田義雄
  • Organizer: 日本数学会総合分科会函数方程式論分科会
  • Place of Presentation: 信州大学松本キャンパス
  • Year and Date: 2011-09-28
• [Presentation] Bifurcation structure of stationary layers for an adsorbate induced phase transition model (2011)
  • Author(s): 久藤衡介、辻川亨
  • Organizer: 日本数学会総合分科会函数方程式論分科会
  • Place of Presentation: 信州大学松本キャンパス
  • Year and Date: 2011-09-28
• [Presentation] Stationary patternsfor an adsorbate-induced phase transitionmodel (2009)
  • Author(s): 久藤衡介,辻川亨
  • Organizer: 日本数学会総合分科会函数方程式論分科会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-26
• [Presentation] Stationary patterns for an adsorbate-induced phase transition model (2009)
  • Author(s): 久藤衡介, 辻川亨
  • Organizer: 日本数学会総合分科会関数方程式分科会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-26
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/~kuto/
• [Remarks]
  • URL: http://matha.e-one.uec.ac.jp/~kuto/index.html
• [Remarks]
  • URL: http://matha.a-one.uec.ac.jp/~kuto
• [Remarks]
  • URL: http://www.fit.ac.jp/-kuto/