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2011 Fiscal Year Final Research Report

Complex Ginzburg-Landau type equations

Research Project

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Project/Area Number 20740079
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
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, 准教授 (60349826)

Project Period (FY) 2008 – 2011
Keywords関数方程式
Research Abstract

The complex Ginzburg-Landau equation is intensively studied both in Mathematics and in Physics. The purpose of this research is to solve some problems including open questions concerning the complex Ginzburg-Landau equation and related equations. More precisely, the problem is to clarify whether solutions to those equations exist or not. Almost all the purpose is achieved, and not only new results improving the previous works are established, but also simple proofs are also successfully given in this research.

  • Research Products

    (26 results)

All 2012 2011 2010 2009 2008

All Journal Article (8 results) (of which Peer Reviewed: 7 results) Presentation (18 results)

  • [Journal Article] Global existence of weak solutions to quasilinear degenerate Keller. Segel systems of parabolic. parabolic type with small data2012

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

      Journal of Differential Equations

      Volume: 252 Pages: 2469-2491

    • Peer Reviewed
  • [Journal Article] Global existence of weak solutions to quasilinear degenerate Keller. Segel systems of parabolic. parabolic type2012

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

      Journal of Differential Equations

      Volume: 252 Pages: 1421-1440

    • Peer Reviewed
  • [Journal Article] Monotonicity method applied to complex Ginzburg-Landau type equations2011

    • Author(s)
      Tomomi Yokota
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 380 Pages: 455-466

    • Peer Reviewed
  • [Journal Article] Cauchy problem for the complex Ginzburg-Landau equation with harmonic oscillator2011

    • Author(s)
      Philippe Clement, Noboru Okazawa, Hiroshi Tamura, Tomomi Yokota
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1746 Pages: 100-111

  • [Journal Article] Square Laplacian perturbed by inverse fourth-power potential. I Self-adjointness(real case)2011

    • Author(s)
      Noboru Okazawa, Hiroshi Tamura, Tomomi Yokota
    • Journal Title

      Proceedings of the Royal Society of Edinburgh Section A-Mathematicas

      Volume: 141A Pages: 409-416

    • Peer Reviewed
  • [Journal Article] Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation2010

    • Author(s)
      Noboru Okazawa, Tomomi Yokota
    • Journal Title

      Discrete and Continuous Dynamical Systemes

      Volume: 28 Pages: 311-341

    • Peer Reviewed
  • [Journal Article] Generation of analytic semigroups by generalized Ornstein. Uhlenbeck operators with potentials2009

    • Author(s)
      Takeshi Kojima, Tomomi Yokota
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 364 Pages: 618-629

    • Peer Reviewed
  • [Journal Article] The complex Ginzburg-Landau equation(an improvement)2008

    • Author(s)
      Tomomi Yokota, Noboru Okazawa
    • Journal Title

      GAKUTO Internat. Ser. Math. Sci. Appl

      Volume: 29 Pages: 463-475

    • Peer Reviewed
  • [Presentation] 全空間における複素Ginzburg-Landau方程式の初期値問題に対するコンパクト性の方法2012

    • Author(s)
      横田智巳
    • Organizer
      日本数学会年会実函数論分科会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
  • [Presentation] Maximal domain of Analyticity for C_0-semigroups generated by elliptic operators in L^p,(II)2012

    • Author(s)
      側島基宏
    • Organizer
      日本数学会年会実函数論分科会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
  • [Presentation] Abstract formulation of energy methods for nonlinear Schrodinger equations2012

    • Author(s)
      鈴木敏行
    • Organizer
      日本数学会年会函数方程式論分科会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
  • [Presentation] 準線形退化放物・放物型Keller-Segel系の小さな初期値に対する大域的弱解の存在2012

    • Author(s)
      石田祥子
    • Organizer
      日本数学会年会函数方程式論分科会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
  • [Presentation] 複素Ginzburg-Landau方程式に対するコンパクト性の方法2012

    • Author(s)
      横田智巳
    • Organizer
      第100回神楽坂解析セミナー
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-01-28
  • [Presentation] A simple approach to the Cauchy problem for complex Ginzburg-Landau equations via compactness methods2011

    • Author(s)
      横田智巳
    • Organizer
      第37回発展方程式研究会
    • Place of Presentation
      岐阜大学
    • Year and Date
      2011-12-24
  • [Presentation] Energy methods for abstract nonlinear Schrodinger equations2011

    • Author(s)
      鈴木敏行
    • Organizer
      第37回発展方程式研究会
    • Place of Presentation
      岐阜大学
    • Year and Date
      2011-12-24
  • [Presentation] Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data2011

    • Author(s)
      石田祥子
    • Organizer
      第37回発展方程式研究会
    • Place of Presentation
      岐阜大学
    • Year and Date
      2011-12-24
  • [Presentation] 逆2乗型ポテンシャル項つき非線形Schrodinger方程式の大域的適切性2011

    • Author(s)
      鈴木敏行
    • Organizer
      日本数学会秋季総合分科会実函数論分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-29
  • [Presentation] 準線形退化Keller-Segel系の大域的弱解の存在2011

    • Author(s)
      石田祥子
    • Organizer
      日本数学会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
  • [Presentation] Maximal domain of Analyticity for C^0-semigroups generated by elliptic operators in L_p2011

    • Author(s)
      側島基宏
    • Organizer
      日本数学会年会実函数論分科会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2011-03-21
  • [Presentation] 準線形退化Keller-Segel系の大域的弱解の存在について2010

    • Author(s)
      石田祥子
    • Organizer
      第36回発展方程式研究会
    • Place of Presentation
      中央大学
    • Year and Date
      2010-12-23
  • [Presentation] Cauchy problem for the complex Ginzburg-Landau equation with harmonic oscillator, Nonlinear evolution equations and related topics to mathematical analysis of a phenomena2010

    • Author(s)
      横田智巳
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-14
  • [Presentation] 特異性をもつポテンシャルつきの4階楕円型作用素の自己共役性とその周辺2010

    • Author(s)
      横田智巳
    • Organizer
      第509回応用解析研究会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-06-19
  • [Presentation] Smoothing effect for complex Ginzburg-Landau type equations with p-Laplacian2010

    • Author(s)
      横田智巳
    • Organizer
      日本数学会年会実函数論分科会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
  • [Presentation] Generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators with Potentials2009

    • Author(s)
      横田智巳
    • Organizer
      日本数学会秋季総合分科会実函数論分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
  • [Presentation] Monotonicity method applied to complex Ginzburg-Landau type equations2009

    • Author(s)
      横田智巳
    • Organizer
      日本数学会秋季総合分科会実函数論分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
  • [Presentation] 複素Ginzburg-Landau方程式のL^p理論に向けて2008

    • Author(s)
      横田智巳
    • Organizer
      日本数学会秋季総合分科会実函数論分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27

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Published: 2013-07-31  

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