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Unified Study of Turing type Instability

Research Project

Project/Area Number 25400171
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionHiroshima University

Principal Investigator

Sakamoto Kunimochi  広島大学, 理学(系)研究科(研究院), 教授 (40243547)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
KeywordsTuring 不安定化 / 境界上の相互作用 / ステクロフ固有値 / ディリクレーノイマン写像 / 拡散系 / 多変数系 / Hopfモードの不安定化 / 臨界曲線 / パターン形成 / 境界相互作用 / Hop モードの不安定化 / Turing 型不安定化 / 拡散輸送 / 不安定化閾値曲線 / 固有値問題 / 特殊関数 / 細胞極性 / Turing 型不安化 / 境界での非対角型物質輸送 / 波動モードの不安定化 / 楕円型固有値問題
Outline of Final Research Achievements

In this project, we have extended the conventional Turing instability mechanism in two directions. In one direction, the usual Turing mechanism for two component closed systems has been extended to multi-component closed systems. In the other direction, The Turing type mechanism has been extended to open systems, in which mass-transfer through the boundary of the system is present.In the Turing mechanisms for the non-conventional Turing instabililty, both steady and oscillatory instability occur even for systems with equal diffusivity, and in this case, the instability threshold is not a simple inmaginary axis, but is a nonlinearly curved. The curve is determined solely by the domain under consideration and the Laplace operator on it.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (15 results)

All 2016 2015 2014 2013 Other

All Journal Article (4 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) (of which Int'l Joint Research: 1 results,  Invited: 7 results)

  • [Journal Article] Destabilization threshold curves for diffusion systems with equal diffusivity under non-diagonal flux boundary conditions2016

    • Author(s)
      K. Sakamoto
    • Journal Title

      Discrete and Continuous Dynamical Systems B

      Volume: 21 Pages: 641-654

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Destabilization of uniform steady states in linear diffusion systems with nonlinear boundary conditions2015

    • Author(s)
      A. Anma, K. Sakamoto
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 64 Pages: 201-207

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Destabilization/Stabilization of Diffusion Systems by Diffusion and Boundary Flux2014

    • Author(s)
      Kunimochi Sakamoto
    • Journal Title

      数理解析研究所講究録

      Volume: 1924 Pages: 30-54

    • Related Report
      2014 Research-status Report
  • [Journal Article] Turing type mechanisms for linear diffusion systems under nondiagonal Robin boundary conditions2013

    • Author(s)
      A. Anma and K. Sakamoto
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 45 Issue: 6 Pages: 3611-2628

    • DOI

      10.1137/130908270

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Diffusion in the bulk and non-diagonal flux on the boundary lead to Turing type instability2016

    • Author(s)
      K. Sakamoto
    • Organizer
      International Conference on Dynamics of Evolution Equations
    • Place of Presentation
      CIRM, Aix-Marseill, Marseille, France
    • Year and Date
      2016-03-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Turing Bifurcations in Diffusion Systems with Nonlinear Boundary Interactions2015

    • Author(s)
      K. Sakamoto
    • Organizer
      Pattern Formation and Dynamics of Solution Structure
    • Place of Presentation
      北海道大学理学研究科
    • Year and Date
      2015-06-26
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Generalized Steklov Eigenvalues for the Laplacian2014

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      Modern Problems in Mathematical Physics
    • Place of Presentation
      Faculty of Physics, Moscow State University, Russia
    • Year and Date
      2014-11-28 – 2014-11-29
    • Related Report
      2014 Research-status Report
  • [Presentation] Periodic traveling waves in a derivative nonlinear Schoedinger equation2014

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      Colloquium at Department of Mathematics, Faculty of Physics, Moscow State University
    • Place of Presentation
      Faculty of Physics, Moscow State University, Russia
    • Year and Date
      2014-11-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Diffusion Equation under Dynamic Boundary Conditions2014

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Universidad Autonoma de Madrid, Spain
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Research-status Report
  • [Presentation] Destabilizations of Turing-type under equal diffusivity2014

    • Author(s)
      Kunimochi Sakamoto
    • Organizer
      Nonlinear Dynamics with Applications to Biology, An NCTS International Conference
    • Place of Presentation
      National Tsing-Hua University, Taiwan
    • Year and Date
      2014-05-28 – 2014-05-30
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Hopf destabilization of nontrivial spatial modes in diffusion systems with equal diffusion rates2014

    • Author(s)
      坂元国望
    • Organizer
      Singuraities arising in Nonlinear Phenomena (SNP2013Winter)
    • Place of Presentation
      関西セミナーハウス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Co-existence by using the geometry of domain2013

    • Author(s)
      坂元国望
    • Organizer
      日本数理生物学会
    • Place of Presentation
      静岡大学(浜松市)
    • Related Report
      2013 Research-status Report
  • [Presentation] Destabilization/Stabilization of Diffusion Systems by Diffusion and Boundary Flux2013

    • Author(s)
      坂元国望
    • Organizer
      非線形現象に現れるパターン形成の数理解析(RIMS研究集会)
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Dirichlet-to-Neumann Map: A useful tool for studying patterns and intefraces2013

    • Author(s)
      坂元国望
    • Organizer
      反応拡散系のパターンダイナミクス
    • Place of Presentation
      富山大学理学部
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Steklov eigenvalue problems arising in diffusion systems under dynamic boundary conditions

    • Author(s)
      坂元国望
    • Organizer
      京都大学非線形偏微分方程式セミナー
    • Place of Presentation
      京都大学理学研究科
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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