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Mathematical analysis of reaction-diffusion system with divergence in vertebrate morphogenesis

Research Project

Project/Area Number 20740058
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionOsaka University

Principal Investigator

NAKAGUCHI Etsushi  Osaka University, 教養部, 准教授 (70304011)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Keywords応用数学 / 数理生物学 / 反応拡散系 / 個体ゆらぎ / モデル化 / 非線形力学系 / 発現制御 / ロバスト性 / 登現制御
Research Abstract

We discussed the modeling and the analysis scheme for individual divergence in the reaction-diffusion system that described the left-right determination process in vertebrate morphogenesis. Moreover, concerning to the theory of morphogenesis dynamics, we studied the existence of global solutions and the structure of attractors of the reaction-diffusion system.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (22 results)

All 2011 2010 2009 2008

All Journal Article (13 results) (of which Peer Reviewed: 6 results) Presentation (7 results) Book (2 results)

  • [Journal Article] Global existence of solutions to a parabolic-parabolic system for chemotaxis with weak degradation2011

    • Author(s)
      E.Nakaguchi, K.Osaki
    • Journal Title

      Nonlinear Analysis : Theory, Method and Applications vol.74, no.1

      Pages: 286-297

    • Related Report
      2010 Final Research Report
  • [Journal Article] Global existence of solutions to a parabolic-parabolic system for chemotaxis with weak degradation2011

    • Author(s)
      E.Nakaguchi, K.Osaki
    • Journal Title

      Nonlinear Analysis : Theory, Methods & Applications

      Volume: 74巻1号 Pages: 286-297

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dimension estimate of global attractors for a chemotaxis-growth system and its discretizations2010

    • Author(s)
      E.Nakaguchi
    • Journal Title

      京都大学数理解析研究所講究録 no.1693

      Pages: 143-150

    • Related Report
      2010 Final Research Report
  • [Journal Article] Attractor dimension and numerical analysis of a chemotaxis-growth system2010

    • Author(s)
      E.Nakaguchi
    • Journal Title

      International Journal of Biomathematics and Biostatistics vol.1, no.1

      Pages: 83-91

    • Related Report
      2010 Final Research Report
  • [Journal Article] Attractor dimension and numerical analysis of a chemotaxis-growth system2010

    • Author(s)
      E.Nakaguchi
    • Journal Title

      International Journal of Biomathematics and Biostatistics

      Volume: 1巻1号 Pages: 83-91

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme2009

    • Author(s)
      M.Efendiev, E.Nakaguchi, W.L.Wendland
    • Journal Title

      Journal of Mathematical Analysis and Applications vol.358, no.1

      Pages: 136-147

    • Related Report
      2010 Final Research Report
  • [Journal Article] Dimension estimate of the global attractor for a semi-discretized chemotaxis-growth system by conservative upwind finite-element scheme2009

    • Author(s)
      M.Efendiev, E.Nakaguchi, W.L.Wendland
    • Journal Title

      Journal of Mathematical Analysis and Applications 358巻1号

      Pages: 136-147

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dimension estimate of the exponential attractor for the chemotaxis-growth system2008

    • Author(s)
      M.Efendiev, E.Nakaguchi, K.Osaki
    • Journal Title

      Glasgow Mathematical Journal vol.50, no.3

      Pages: 483-497

    • Related Report
      2010 Final Research Report
  • [Journal Article] On a new dimension estimate of the global attractor for chemotaxis-growth systems2008

    • Author(s)
      E.Nakaguchi, M.Efendiev
    • Journal Title

      Osaka Journal of Mathematics vol.45, no.2

      Pages: 273-281

    • NAID

      120004844624

    • Related Report
      2010 Final Research Report
  • [Journal Article] 反応拡散方程式のシミュレーションに現れる不安定振動パターン2008

    • Author(s)
      中口悦史
    • Journal Title

      京都大学数理解析研究所講究録 no.1597

      Pages: 10-14

    • Related Report
      2010 Final Research Report
  • [Journal Article] 反応拡散方程式のシミュレーションに現れる不安定振動パターン2008

    • Author(s)
      中口悦史
    • Journal Title

      京都大学数理解析研究所講究録 1597号

      Pages: 10-14

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a new dimension estimate of the global attractor for chemotaxis-growth systems2008

    • Author(s)
      E. Nakaguchi and M. Efendiev
    • Journal Title

      Osaka Journal of Mathematics 45巻2号

      Pages: 273-281

    • NAID

      120004844624

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dimension estimate of the exponential attractor for the chemotaxis-growth system2008

    • Author(s)
      M. Efendiev, E. Nakaguchi and K. Osaki
    • Journal Title

      Glasgow Mathematical Journal 50巻3号

      Pages: 483-497

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 弱い減衰項を持つ走化性方程式の大域解の存在2011

    • Author(s)
      大崎浩一, 中口悦史
    • Organizer
      日本数学会2011年度年会函数方程式論分科会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-22
    • Related Report
      2010 Final Research Report
  • [Presentation] 弱い減衰項を持つ走化性方程式の大域解の存在2011

    • Author(s)
      中口悦史
    • Organizer
      日本数学会2011年度年会函数方程式論分科会
    • Place of Presentation
      早稲田大学理工学術院
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report
  • [Presentation] 弱い減衰を持つ走化性・増殖方程式の解の大域的存在2011

    • Author(s)
      中口悦史
    • Organizer
      第93回神楽坂解析セミナー
    • Place of Presentation
      東京理科大学神楽坂校舎(東京都新宿区)
    • Year and Date
      2011-01-22
    • Related Report
      2010 Final Research Report
  • [Presentation] マウス胚の左右軸形成過程を数理の目で観る2010

    • Author(s)
      中口悦史
    • Organizer
      明治大学グローバルCOEプログラム【現象数理学の形成と発展】第7回現象数理若手シンポジウム「細胞・腫瘍の数理ーモデル・解析・シミュレーションー」
    • Place of Presentation
      明治大学生田校舎(神奈川県川崎市多摩区)
    • Year and Date
      2010-11-06
    • Related Report
      2010 Final Research Report
  • [Presentation] 形態形成過程を数理の目で観る2009

    • Author(s)
      中口悦史
    • Organizer
      第22回大学院医歯学総合研究科大学院セミナー「生命科学研究のフロンティア」
    • Place of Presentation
      東京医科歯科大学歯学部特別講堂
    • Year and Date
      2009-12-17
    • Related Report
      2010 Final Research Report
  • [Presentation] 走化性・増殖方程式とその離散系のグローバルアトラクタに対する次元評価2009

    • Author(s)
      中口悦史
    • Organizer
      RIMS 研究集会「非線形発展方程式と現象の数理」
    • Place of Presentation
      京都大学楽友会館
    • Year and Date
      2009-10-22
    • Related Report
      2010 Final Research Report
  • [Presentation] 走化性・増殖方程式とその離散系のグローバルアトラクタに対する次元評価2009

    • Author(s)
      中口悦史
    • Organizer
      京都大学数理解析研究所研究集会「非線形発展方程式と現象の数理」
    • Place of Presentation
      京都大学楽友会館
    • Year and Date
      2009-10-22
    • Related Report
      2009 Annual Research Report
  • [Book] Proceedings of International Conference on Nonlinear Phenomena with Energy Dissipation : Mathematical Analysis, Modelling and Simulation, GAKUTO International Series Mathematical Sciences and Applications("Comparison of approximation schemes for chemotaxis-growth system via dimensions of global attractors")(P.Colli et al.(eds.))vol.29, Tokyo2008

    • Author(s)
      E.Nakaguchi, M.Efendiev, W.L.Wendland
    • Publisher
      Gakkotosho
    • Related Report
      2010 Final Research Report
  • [Book] Nonlinear Phenomena with Energy Dissipation : Mathematical Analysis, Modelling and Simulation2008

    • Author(s)
      P. Colli et.al. (eds.)
    • Publisher
      Gakkotosho
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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