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Complex Ginzburg-Landau type equations

Research Project

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
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords関数方程式 / 複素ギンツブルク・ランダウ型方程式 / 非線形シュレディンガー型方程式 / 準線形退化型ケラー・シーゲル方程式 / 大域的強解 / 爆発 / 解の存在と一意性 / 平滑化作用 / 複素ギンツブルク・ランダウ方程式 / レゾルベント問題
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.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (47 results)

All 2012 2011 2010 2009 2008

All Journal Article (22 results) (of which Peer Reviewed: 19 results) Presentation (25 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

    • Related Report
      2011 Final Research Report
    • 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

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type2012

    • Author(s)
      Sachiko Ishida
    • Journal Title

      JOURNAL OF DIFFERENTIAL EQUATIONS

      Volume: 252 Issue: 2 Pages: 1421-1440

    • DOI

      10.1016/j.jde.2011.02.012

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global existence of weak solutions to quasilinear degenerate Keller-Segel systems of parabolic-parabolic type with small data2012

    • Author(s)
      Sachiko Ishida
    • Journal Title

      JOURNAL OF DIFFERENTIAL EQUATIONS

      Volume: 252 Issue: 3 Pages: 2469-2491

    • DOI

      10.1016/j.jde.2011.08.047

    • Related Report
      2011 Annual Research Report
    • 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

    • Related Report
      2011 Final Research Report
    • 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

    • Related Report
      2011 Final Research Report
  • [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

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Square Laplacian perturbed by inverse fourth-power potential. I Self-adjointness (real case)2011

    • Author(s)
      Noboru Okazawa
    • Journal Title

      PROCEEDINGS OF THE ROYAL SOCIEIY OF EDINBURGH SECTION A-MATHEMATICS

      Volume: 141A Pages: 409-416

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cauchy problem for the complex Ginzburg-Landau equation with harmonic oscillator2011

    • Author(s)
      Philippe Clement
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1,746 Pages: 100-111

    • Related Report
      2011 Annual Research Report
  • [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 Issue: 2 Pages: 455-466

    • DOI

      10.1016/j.jmaa.2011.04.001

    • Related Report
      2011 Annual Research Report
    • 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

    • Related Report
      2011 Final Research Report
    • 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 28

      Pages: 311-341

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Subdifferential operator approach to strong wellposedness of the complex Ginzburg-Landau equation2010

    • Author(s)
      Noboru Okazawa
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: 28 Pages: 311-341

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Remarks on linear Schrodinger evolution equations with Coulomb potential with moving center2010

    • Author(s)
      Noboru Okazawa
    • Journal Title

      SUT Journal of Mathematics

      Volume: 46 Pages: 155-176

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Higher-order Schrodinger operators with singular potentials2010

    • Author(s)
      Noboru Okazawa
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1693 Pages: 11-27

    • Related Report
      2010 Annual Research Report
  • [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

    • Related Report
      2011 Final Research Report
    • 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 364

      Pages: 618-629

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Generation of analytic semigroups by generalized Ornstein-Uhlenbeck operators with potentials2009

    • Author(s)
      Takeshi Kojima
    • Journal Title

      Journal of Mathematical Analysis and Applications 364

      Pages: 618-629

    • Related Report
      2009 Annual Research Report
    • 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

    • Related Report
      2011 Final Research Report
    • 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. 29

      Pages: 463-475

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The complex Ginzburg-Landau equation (an improvement)2008

    • Author(s)
      Tomomi Yokota
    • Journal Title

      GAKUTO Internat. Ser. Math. Sci. Appl 29

      Pages: 463-475

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quasi-m-accretivity of SchrOdinger operators with singular first-order coefficients2008

    • Author(s)
      Noboru Okazawa
    • Journal Title

      DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 22

      Pages: 1081-1090

    • Related Report
      2008 Annual Research Report
    • 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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] bstract formulation of energy methods for nonlinear Schrodinger equation2012

    • 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
    • Related Report
      2011 Annual Research Report
  • [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
    • Related Report
      2011 Annual Research Report
  • [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
    • Related Report
      2011 Annual Research Report
  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [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
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [Presentation] Cauchy problem for the complex Ginzburg-Landau equation with harmonic oscillator2010

    • Author(s)
      横田智巳
    • Organizer
      Nonlinear evolution equations and related topics to mathematical analysis of a phenomena
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-10-14
    • Related Report
      2010 Annual Research Report 2010 Self-evaluation Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [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
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report 2009 Annual Research Report
  • [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
    • Related Report
      2009 Annual Research Report
  • [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
    • Related Report
      2011 Final Research Report
  • [Presentation] 複素Ginzburg-Landau方程式のLp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
    • Related Report
      2010 Self-evaluation Report
  • [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
    • Related Report
      2008 Annual Research Report

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

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