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Study of chemotaxis models and complex Ginzburg-Landau type equations

Research Project

Project/Area Number 16K05182
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionTokyo University of Science

Principal Investigator

Yokota Tomomi  東京理科大学, 理学部第一部数学科, 教授 (60349826)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords走化性方程式 / 解の存在と有界性 / 解の漸近挙動 / 複素ギンツブルク・ランダウ方程式 / 関数解析学 / 関数方程式論
Outline of Final Research Achievements

In this research we made mathematical studies of two themes, ``Global-in-time solvability and asymptotic behavior of solutions to chemotaxis models'' and ``Global-in-time solvability and asymptotic behavior of solutions to complex Ginzburg-Landau type equations''. There is some common property in the equations dealt with in these two themes and we made a study by using a synergistic effect from it. As to the former theme, we showed that the solution of the equation converges to a constant as time passes. As to the latter theme, we could show that the solution of the equation vanishes after some time.

Academic Significance and Societal Importance of the Research Achievements

走化性モデルは、餌に集中する生物や癌浸潤現象等の身近な現象を記述するモデルであり、数学的に定式化された方程式の解の存在や性質を明らかにすることは生物学的にも数学的にも重要である。複素ギンツブルク・ランダウ方程式についても、物理学における基本的なモデルであり、解の性質を数学的に研究することは重要である。本研究課題では、走化性モデルと複素ギンツブルク・ランダウ方程式の数学的研究を行い、一般性のある幾つかの研究成果を得た。それらは様々な現象解明の基礎になると考えられる。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (22 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (2 results) Journal Article (9 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 9 results,  Acknowledgement Compliant: 1 results) Presentation (10 results) (of which Int'l Joint Research: 6 results,  Invited: 6 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Paderborn University(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Paderborn University(Germany)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Stabilization in the logarithmic Keller-Segel system2018

    • Author(s)
      Winkler Michael、Yokota Tomomi
    • Journal Title

      Nonlinear Analysis

      Volume: 170 Pages: 123-141

    • DOI

      10.1016/j.na.2018.01.002

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Finite-time blow-up for quasilinear degenerate Keller--Segel systems of parabolic-parabolic type2018

    • Author(s)
      Hashira Takahiro、Ishida Sachiko、Yokota Tomomi
    • Journal Title

      Journal of Differential Equations

      Volume: 264 Issue: 10 Pages: 6459-6485

    • DOI

      10.1016/j.jde.2018.01.038

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems on unbounded domains via Cauchy's criterion2018

    • Author(s)
      Fukao Takeshi、Kurima Shunsuke、Yokota Tomomi
    • Journal Title

      Mathematical Methods in the Applied Sciences

      Volume: 41 Issue: 7 Pages: 2590-2601

    • DOI

      10.1002/mma.4760

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence and boundedness in a chemotaxis-haptotaxis system with signal-dependent sensitivity2018

    • Author(s)
      Mizukami Masaaki、Otsuka Hirohiko、Yokota Tomomi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 464 Issue: 1 Pages: 354-369

    • DOI

      10.1016/j.jmaa.2018.04.002

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Large time behavior in a chemotaxis model with nonlinear general diffusion for tumor invasion2018

    • Author(s)
      Fujie Kentarou、Ishida Sachiko、Ito Akio、Yokota Tomomi
    • Journal Title

      Funkcialaj Ekvacioj. Serio Internacia

      Volume: 61 Pages: 37-80

    • NAID

      130006726044

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness in a chemotaxis model with nonlinear diffusion and logistic type source for tumor invasion2018

    • Author(s)
      Osawa Ryosuke、Yokota Tomomi
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: 27 Pages: 224-240

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Boundedness and stabilization in a two-dimensional two-species chemotaxis-Navier?Stokes system with competitive kinetics2017

    • Author(s)
      Hirata Misaki、Kurima Shunsuke、Mizukami Masaaki、Yokota Tomomi
    • Journal Title

      Journal of Differential Equations

      Volume: 263 Issue: 1 Pages: 470-490

    • DOI

      10.1016/j.jde.2017.02.045

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity2017

    • Author(s)
      Mizukami Masaaki、Yokota Tomomi
    • Journal Title

      Mathematische Nachrichten

      Volume: 290 Issue: 16 Pages: 2648-2660

    • DOI

      10.1002/mana.201600399

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion2016

    • Author(s)
      Masaaki Mizukami, Tomomi Yokota
    • Journal Title

      JOURNAL OF DIFFERENTIAL EQUATIONS

      Volume: 261 Issue: 5 Pages: 2650-2669

    • DOI

      10.1016/j.jde.2016.05.008

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Effect of nonlinear diffusion on a lower bound for the blow-up time for solutions of a fully parabolic chemotaxis system2019

    • Author(s)
      西野瑛登, 横田智巳
    • Organizer
      日本数学会年会 函数方程式論分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Remarks on boundedness and stabilization in a fully parabolic Keller-Segel system with signal-dependent sensitivity2018

    • Author(s)
      Tomomi Yokota
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundedness in the Keller-Segel system with signal-dependent sensitivity2018

    • Author(s)
      Tomomi Yokota
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundedness in a chemotaxis-haptotaxis system with signal-dependent sensitivity2018

    • Author(s)
      水上雅昭、大塚裕彦、横田智巳
    • Organizer
      日本数学会秋期総合分科会 実函数論分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Explicit lower bound for the blow-up time for solutions of a fully parabolic chemotaxis system with nonlinear diffusion2018

    • Author(s)
      西野瑛登, 横田智巳
    • Organizer
      第44回発展方程式研究会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Asymptotic stability in a two-dimensional two-species chemotaxis-Navier--Stokes system with competitive kinetics2017

    • Author(s)
      Tomomi Yokota
    • Organizer
      Equadiff 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Boundedness in some chemotaxis systems2017

    • Author(s)
      Tomomi Yokota
    • Organizer
      Partial Differential Equations and Applied Mathematics Seminar
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundedness in fully parabolic Keller--Segel systems2016

    • Author(s)
      Tomomi Yokota
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      京都大学理学部6号館401号室
    • Year and Date
      2016-12-18
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Mathematical analysis of a chemotaxis model via maximal regularity2016

    • Author(s)
      Tomomi Yokota
    • Organizer
      The 41st Sapporo Symposium on Partial Differential Equations
    • Place of Presentation
      Conference Hall, Hokkaido University
    • Year and Date
      2016-08-08
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundedness in a quasilinear parabolic-parabolic Keller-Segel system via maximal regularity2016

    • Author(s)
      Sachiko Ishida, Tomomi Yokota
    • Organizer
      The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Hyatt Regency Orlando, Orlando, Hyatt Regency Orlando, USA
    • Year and Date
      2016-07-03
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] The 4th International Workshop on Mathematical Analysis of Chemotaxis2019

    • Related Report
      2018 Annual Research Report

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Published: 2016-04-21   Modified: 2020-03-30  

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