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Studies on well-posedness for semilinear evolution equations with constraints and their applications

Research Project

Project/Area Number 20540173
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionHiroshima University

Principal Investigator

MATSUMOTO Toshitaka  Hiroshima University, 大学院・理学研究科, 助教 (20229561)

Co-Investigator(Kenkyū-buntansha) KOBAYASHI Yoshikazu  中央大学, 理工学部, 教授 (80092691)
Co-Investigator(Renkei-kenkyūsha) TANAKA Naoki  静岡大学, 理学部, 教授 (00207119)
OHARU Shinnosuke  中央大学, 理工学部, 教授 (40063721)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords制約条件 / 半線形方程式 / 適切性 / リプシッツ作用素半群 / 正則性 / 近似理論 / 積公式 / Lipschitz作用素半群 / Lipschitz半群
Research Abstract

operators and well-posedness for semilinear evolution equations. We extended the former results on the generation of quasi-contractive semigroups and applied the obtained results to show the well-posedness of the complex Ginzburg-Landau equation, drift-diffusion equations, 2-dimensional Navier-Stokes equation and strongly degenerate parabolic equations. We also obtained a convergence theorem, an approximation theorem and product formulas of Chernoff type for semigroups of Lipschitz operators.

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 Other

All Journal Article (9 results) (of which Peer Reviewed: 7 results) Presentation (12 results) Remarks (1 results)

  • [Journal Article] BV-entropy solutions to strongly degenerate parabolic equations2010

    • Author(s)
      H.Watanabe, S.Oharu
    • Journal Title

      Adv.Differential Equations 15

      Pages: 757-800

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Well-posedness for the complex Ginzburg-Landau equations2010

    • Author(s)
      T.Matsumoto, N.Tanaka
    • Journal Title

      GAKUTO Internat.Ser.Math.Sci.Appl. 32

      Pages: 429-442

    • Related Report
      2010 Final Research Report
  • [Journal Article] A Lipschitz semigroup approach to two-dimensional Navier-Stokes equations2010

    • Author(s)
      Y.Kobayashi, N.Tanaka
    • Journal Title

      Nonlinear Anal.TMA 72

      Pages: 1820-1828

    • NAID

      120001820434

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Well-posedness for the complex Ginzburg-Landau equations2010

    • Author(s)
      T.Matsumoto, N.Tanaka
    • Journal Title

      GAKUTO Internat.Ser.Math.Sci.Appl.

      Volume: 32 Pages: 429-442

    • Related Report
      2010 Annual Research Report
  • [Journal Article] BV-entropy solutions to strongly degenerate parabolic equations2010

    • Author(s)
      H.Watanabe, S.Oharu
    • Journal Title

      Adv.Differential Equations

      Volume: 15 Pages: 757-800

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Lipschitz semigroup approach to two-dimensional Navier-Stokes equations2010

    • Author(s)
      Y.Kobayashi, N.Tanaka
    • Journal Title

      Nonlinear Analysis T.M.A VOL.72

      Pages: 1820-1828

    • NAID

      120001820434

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lipschitz semigroup approach to drift-diffusion systems2009

    • Author(s)
      T.Matsumoto, N.Tanaka
    • Journal Title

      RIMS Kokyuroku Bessatsu B15

      Pages: 147-177

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lipschitz semigroup approach to drift-diffusion systems2009

    • Author(s)
      T.Matsumoto, N.Tanaka
    • Journal Title

      RIMS Kokyuroku Bessatsu VOL.B15

      Pages: 147-177

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Product formula for semigroups of Lipschitz operators associated with semilinear evolution equations of parabolic type

    • Author(s)
      Toshitaka Matsumoto, Naoki Tanaka
    • Journal Title

      J.Approx.Theory (印刷中)

    • NAID

      120003368391

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] リプシッツ作用素半群の近似定理2011

    • Author(s)
      小林良和, 田中直樹
    • Organizer
      日本数学会
    • Place of Presentation
      早稲田大学(東京都新宿区)
    • Year and Date
      2011-03-21
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 半線形放物型方程式に付随するリプシッツ作用素半群に対する積公式2010

    • Author(s)
      松本敏隆, 田中直樹
    • Organizer
      日本数学会
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] リプシッツ作用素半群と偏微分方程式への応用2010

    • Author(s)
      小林良和
    • Organizer
      日本数学会
    • Place of Presentation
      慶応大学(横浜市)
    • Year and Date
      2010-03-26
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Characterization and approximation-solvability of semilinear parabolic evolution equations2009

    • Author(s)
      松本敏隆, 大春愼之助
    • Organizer
      第35回発展方程式研究会
    • Place of Presentation
      中央大学(東京都文京区)
    • Year and Date
      2009-12-24
    • Related Report
      2010 Final Research Report
  • [Presentation] 複素Ginzburg-Landau方程式のLp適切性2009

    • Author(s)
      松本敏隆
    • Organizer
      愛媛大学解析セミナー
    • Place of Presentation
      愛媛大学(松山市)
    • Year and Date
      2009-11-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Well-posedness of the complex Ginzburg-Landau equation in L^p2009

    • Author(s)
      松本敏隆
    • Organizer
      RIMS研究集会「非線形発展方程式と現象の数理」
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2009-10-20
    • Related Report
      2010 Final Research Report
  • [Presentation] 複素Ginzburg-Landau方程式のL^p適切性2009

    • Author(s)
      松本敏隆, 田中直樹
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学(豊中市)
    • Year and Date
      2009-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Solvability of strongly degenerate diffusion systems with nonlocal convective terms2009

    • Author(s)
      大春愼之助, 渡邉紘
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学(豊中市)
    • Year and Date
      2009-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] 複素 Ginzburg-Landau 方程式のL^p適切性2009

    • Author(s)
      松本敏隆, 田中直樹
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Nonlinear evolution operators for strongly degenerate convective diffusion equations2009

    • Author(s)
      大春愼之助, 渡邉紘
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学(東京都目黒区)
    • Year and Date
      2009-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] Drift-diffusion方程式へのリプシッツ作用素半群論的接近法2008

    • Author(s)
      松本敏隆, 田中直樹
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2008-09-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Drift-diffusion方程式へのリプシッツ作用素半群論的接近法2008

    • Author(s)
      松本 敏隆, 田中 直樹
    • Organizer
      日本数学会 2008年度総合分科会
    • Place of Presentation
      東京都目黒区
    • Year and Date
      2008-09-27
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report

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

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