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Study of quasilinear degenerate Keller-Segel systems and complex Ginzburg-Landau type equations'

Research Project

Project/Area Number 25400119
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, 准教授 (60349826)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords解の存在 / 解の漸近挙動 / ケラー・シーゲル系 / 複素ギンツブルク・ランダウ方程式 / 解の有界性 / 解の消滅 / 解の挙動 / 国際研究者交流(ドイツ)
Outline of Final Research Achievements

In this research, we made mathematical analysis to ``Global-in-time solvability and asymptotic behavior of solutions in quasilinear degenerate Keller-Segel systems'' and `` Global-in-time solvability and asymptotic behavior of solutions in complex Ginzburg-Landau type equations'' as main themes. The equations dealt with in these two themes are formally different, but there is a common in terms of parabolic equations. As to the former theme, we not only succeeded in showing boundedness of solutions left as an open problem but also obtained the same results for related equations. As to the latter theme, we succeeded in obtaining a precise result on blow-up and extinction of solutions.

Report

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

    (24 results)

All 2016 2015 2014 2013 Other

All Journal Article (12 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 12 results,  Acknowledgement Compliant: 7 results) Presentation (12 results) (of which Int'l Joint Research: 2 results,  Invited: 11 results)

  • [Journal Article] Stabilization in a chemotaxis model for tumor invasion2016

    • Author(s)
      Kentarou Fujie, Akio Ito, Michael Winkler, Tomomi Yokota
    • Journal Title

      DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

      Volume: 36 Issue: 1 Pages: 151-169

    • DOI

      10.3934/dcds.2016.36.151

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Existence and decay estimates of solutions to complex Ginzburg-Landau type equations2016

    • Author(s)
      Daisuke Shimotsuma, Tomomi Yokota, Kentarou Yoshii
    • Journal Title

      JOURNAL OF DIFFERENTIAL EQUATIONS

      Volume: 260 Issue: 3 Pages: 3119-3149

    • DOI

      10.1016/j.jde.2015.10.030

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Boundedness of solutions to parabolic-elliptic Keller-Segel systems with signal-dependent sensitivity2015

    • Author(s)
      Kentarou Fujie, Michael Winkler, Tomomi Yokota
    • Journal Title

      MATHEMATICAL METHODS IN THE APPLIED SCIENCES

      Volume: 38 Issue: 6 Pages: 1212-1224

    • DOI

      10.1002/mma.3149

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Cauchy problem for the complex Ginzburg-Landau type equation with L^p-initial data2014

    • Author(s)
      Daisuke Shimotsuma, Tomomi Yokota, Kentarou Yoshii
    • Journal Title

      Mathematica Bohemica

      Volume: 139 Pages: 353-361

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity2014

    • Author(s)
      Kentarou Fujie, Tomomi Yokota
    • Journal Title

      Mathematica Bohemica

      Volume: 139 Pages: 639-647

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity2014

    • Author(s)
      Kentarou Fujie, Michael Winkler, Tomomi Yokota
    • Journal Title

      NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

      Volume: 109 Pages: 56-71

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Existence of solutions to chemotaxis dynamics with Lipschitz diffusion and superlinear growth2014

    • Author(s)
      Tomomi Yokota, Noriaki Yoshino
    • Journal Title

      JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

      Volume: 419 Pages: 756-774

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Possibility of the existence of blow-up solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type2013

    • Author(s)
      Sachiko Ishida, Takashi Ono, Tomomi Yokota
    • Journal Title

      MATHEMATICAL METHODS IN THE APPLIED SCIENCES

      Volume: 36 Issue: 7 Pages: 745-760

    • DOI

      10.1002/mma.2622

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type2013

    • Author(s)
      Sachiko Ishida, Tomomi Yokota
    • Journal Title

      DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

      Volume: 18 Issue: 10 Pages: 2569-2596

    • DOI

      10.3934/dcdsb.2013.18.2569

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Gradient estimate for solutions to quasilinear non-degenerate Keller-Segel systems on R^N2013

    • Author(s)
      Sachiko Ishida, Yusuke Maeda, Tomomi Yokota
    • Journal Title

      DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

      Volume: 18 Issue: 10 Pages: 2537-2568

    • DOI

      10.3934/dcdsb.2013.18.2537

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A direct approach to generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators in weighted L^p spaces2013

    • Author(s)
      Motohiro Sobajima, Tomomi Yokota
    • Journal Title

      JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

      Volume: 403 Issue: 2 Pages: 606-618

    • DOI

      10.1016/j.jmaa.2013.02.054

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence of solutions to some degenerate parabolic equation associated with the p-Laplacian in the critical case2013

    • Author(s)
      Yoji Yamashita, Tomomi Yokota
    • Journal Title

      Nonlinear Analysis

      Volume: 93 Pages: 168-180

    • DOI

      10.1016/j.na.2013.07.035

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Boundedness of solutions to a quasilinear degenerate Keller-Segel system with subcritical sensitivity2015

    • Author(s)
      Tomomi Yokota
    • Organizer
      The 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015)
    • Place of Presentation
      China National Convention Center, Beijing, China
    • Year and Date
      2015-08-12
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Global existence and boundedness in a quasilinear degenerate Keller-Segel system2015

    • Author(s)
      Tomomi Yokota
    • Organizer
      Equadiff 2015
    • Place of Presentation
      Lyon, France
    • Year and Date
      2015-07-07
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 準線形退化放物・放物型Keller-Segel系の時間大域的弱解の存在と有界性: 最大正則性原理からのアプローチ2015

    • Author(s)
      横田智巳
    • Organizer
      応用解析セミナー
    • Place of Presentation
      東京大学 数理科学研究科棟(東京都・目黒区)
    • Year and Date
      2015-06-11
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Blow-up for a complex Ginzburg-Landau equation focusing on the parabolicity2014

    • Author(s)
      Tomomi Yokota
    • Organizer
      59th Congress of the Indian Society Of Theoretical and Applied Mechanics
    • Place of Presentation
      Alliance University, India
    • Year and Date
      2014-12-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Nonlinear m-accretive operator approach to parabolic-elliptic chemotaxis systems with superlinear growth2014

    • Author(s)
      Tomomi Yokota, Noriaki Yoshino
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Madrid, Universidad Autonoma de Madrid
    • Year and Date
      2014-07-10
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Blow-up in H^1-norm for a special type of complex Ginzburg-Landau equations2014

    • Author(s)
      Tomomi Yokota, Takuya Tomidokoro
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Madrid, Universidad Autonoma de Madrid
    • Year and Date
      2014-07-08
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Blow-up of solutions to a special type of complex Ginzburg-Landau equations2014

    • Author(s)
      Tomomi Yokota
    • Organizer
      Conference on Partial Differential Equations
    • Place of Presentation
      Monastery of Novacella, Italy
    • Year and Date
      2014-05-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Boundedness of solutions to parabolic-elliptic Keller-Segel systems

    • Author(s)
      Kentarou Fujie, Michael Winkler, Tomomi Yokota
    • Organizer
      Equadiff 13
    • Place of Presentation
      Charles University in Prague
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Charles University in Prague

    • Author(s)
      Tomomi Yokota
    • Organizer
      One Forum, Two Cities 2013: Aspect of Nonlinear PDEs
    • Place of Presentation
      Waseda University
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A priori estimates for chemotaxis systems

    • Author(s)
      Tomomi Yokota
    • Organizer
      New Role of the Theory of Abstract Evolution Equations -From a Point of View Overlooking the Individual Partial Differential Eqations-
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A priori estimates for solutions to several kinds of Keller-Segel systems

    • Author(s)
      Tomomi Yokota
    • Organizer
      NCTS Mathematics Division
    • Place of Presentation
      Tamkang University, Tamsui Campus, Taipei
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 走化性方程式系の解のアプリオリ評価

    • Author(s)
      横田 智巳
    • Organizer
      第15回さいたま数理解析セミナー
    • Place of Presentation
      大宮ソニックシティ5階 埼玉大学サテライトキャンパス
    • Related Report
      2013 Research-status Report
    • Invited

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

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