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Research on evolution equations involving nonlinear Laplace operators

Research Project

Project/Area Number 19740073
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionShibaura Institute of Technology

Principal Investigator

AKAGI Goro  Shibaura Institute of Technology, システム理工学部, 准教授 (40433768)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,440,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥540,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywords関数方程式 / 非線形偏微分方程式 / 関数方程式論 / 関数解析学 / 放物型方程式 / 非線形解析 / 非線形拡散 / 解の漸近挙動 / 変分法 / 安定性解析
Research Abstract

Sufficient conditions for the existence of local (in time) solutions of some evolution equations involving p-Laplace operators are obtained. Moreover, the well-posedness of some evolution equation involving the infinity-Laplace operator is proved, and furthermore, the asymptotic behaviors (e.g., decay rates) of solutions are also revealed. Finally, a couple of effective methods are established in order to construct solutions and analyze their large-time behaviors for evolution equations involving nonlinear Laplace operators through this research project.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (34 results)

All 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 12 results) Presentation (14 results) Remarks (7 results)

  • [Journal Article] Ulisse Stefanelli, A variational principle for doubly nonlinear evolution2010

    • Author(s)
      Goro Akagi
    • Journal Title

      Applied Mathematics Letters

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On some doubly nonlinear parabolic equations2010

    • Author(s)
      Goro Akagi
    • Journal Title

      Current Advances in Nonlinear Analysis and Related Topics, GAKUTO International Series, Mathematical Sciences and Applications 32

      Pages: 239-254

    • Related Report
      2009 Final Research Report
  • [Journal Article] Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian2009

    • Author(s)
      Goro Akagi, Petri Juutinen, Ryuji Kajikiya
    • Journal Title

      Mathematische Annalen vol.343,no.4

      Pages: 921-953

    • NAID

      120005372395

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy solutions of the Cauchy-Neumann problem for porous medium equations2009

    • Author(s)
      Goro Akagi
    • Journal Title

      The Seventh International Conference on Dynamical Systems and Differential Equations, a supplement volume of Discrete and Continuous Dynamical Systems

      Pages: 1-10

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy solutions of the Cauchy-Neumann problem for porous medium equations2009

    • Author(s)
      Goro Akagi
    • Journal Title

      Discrete and Continuous Dynamical Systems 増刊号

      Pages: 1-10

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian2009

    • Author(s)
      Goro Akagi, Petri Juutinen and Ryuji Kajikiya
    • Journal Title

      Mathematische Annalen 343

      Pages: 921-953

    • NAID

      120005372395

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian2008

    • Author(s)
      Goro Akagi, Kazumasa Suzuki
    • Journal Title

      Calculus of Variations and Partial Differential Equations vol.31,no.4

      Pages: 457-471

    • NAID

      120005372386

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Doubly nonlinear evolution equations in reflexive Banach spaces2008

    • Author(s)
      Goro Akagi
    • Journal Title

      Nonlinear Phenomena with Energy Dissipation, GAKUTO International Series, Mathematical Sciences and Applications 29

      Pages: 19-36

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of viscosity solutions for a degenerate parabolic equation associated with the infinity-Laplacian2008

    • Author(s)
      Goro, Akagi・Kazumasa, Suzuki
    • Journal Title

      Calculus of Variations and Partial Differential Equations 31

      Pages: 457-471

    • NAID

      120005372386

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local existence of solutions to some degenerate parabolic equation associated with the p-Laplacian2007

    • Author(s)
      Goro Akagi
    • Journal Title

      Journal of Differential Equations vol.241,2007,no.2

      Pages: 359-385

    • NAID

      120005372394

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a certain degenerate nonlinear parabolic equation associated with the infinity-Laplacian2007

    • Author(s)
      Goro Akagi, Kazumasa Suzuki
    • Journal Title

      The Sixth International Conference on Dynamical Systems and Differential Equations, a supplement volume of Discrete and Continuous Dynamical Systems

      Pages: 18-27

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Doubly nonlinear evolution equations with non-monotone perturbations2007

    • Author(s)
      Goro Akagi
    • Journal Title

      Proc. Appl. Math. Mech. vol.7,no.1

      Pages: 2040047-2040048

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Local existense of solutions to some degenerate parabolic equation associated with the p-Laplacian2007

    • Author(s)
      Goro, Akagi
    • Journal Title

      Journal of Differential Equations 241

      Pages: 359-385

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Maximal monotonicity for the sum of two maximal monotone operators in Lp-spaces2010

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会2010年度年会, 実関数論分科会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic profiles of sign-changing solutions for parabolic equations associated with p-Laplacian2010

    • Author(s)
      赤木剛朗, 梶木屋龍治
    • Organizer
      日本数学会2010年度年会, 関数方程式論分科会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic profiles of sign-changing solutions for parabolic equations associated with p-Laplacian2010

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Maximal monotonicity for the sum of two maximal monotone operators in Lp-spaces2010

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Energy solutions of porous medium equations with Neumann boundary conditions2009

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会2009年度年会, 実関数論分科会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Energy solutions of porous medium equations with Neumann boundary conditions2009

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] On generalized Allen-Cahn equations2008

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会2008年度秋期総合分科会, 実関数論分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
    • Related Report
      2009 Final Research Report
  • [Presentation] On generalized Allen-Cahn equations2008

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Asymptotic behavior of solutions for a degenerate parabolic equation with inhomogeneous Dirichlet data2008

    • Author(s)
      赤木剛朗, Petri Juutinen, 梶木屋龍治
    • Organizer
      日本数学会2008年度秋期総合分科会, 関数方程式論分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic behavior of solutions for a degenerate parabolic equation with inhomogeneous Dirichlet data2008

    • Author(s)
      赤木剛朗, PetriJuutinen, 梶木屋龍治
    • Organizer
      日本数学会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Generalized semiflows and global attractors for a nonlinear evolution inclusion2008

    • Author(s)
      赤木剛朗
    • Organizer
      日本数学会2008年度年会, 実関数論分科会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalized semiflows and global attractors for a nonlinear evolution inclusion2008

    • Author(s)
      赤木 剛朗
    • Organizer
      日本数学会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic behavior of viscosity solutions for a parabolic equation involving the infinity-Laplacian2007

    • Author(s)
      赤木剛朗, 梶木屋龍治
    • Organizer
      日本数学会2007年度秋期総合分科会, 関数方程式論分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic behavior of viscosity solutions for a parabolic equation involing the infinity-Laplacian2007

    • Author(s)
      赤木 剛朗・梶木屋 龍治
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Remarks] 個人

    • URL

      http://www.mcs.se.shibaura-it.ac.jp/~goro/

    • Related Report
      2009 Final Research Report
  • [Remarks] 第31回発展方程式若手セミナー

    • URL

      http://www.mcs.se.shibaura-it.ac.jp/wakate31/

    • Related Report
      2009 Final Research Report
  • [Remarks] 国際会議「Nonlinear Evolution Equations and Related Topics」

    • URL

      http://www.mcs.se.shibaura-it.ac.jp/conf/

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.mcs.se.shibaura-it-ac.jp/~goro/achievement.html

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.mcs.se.shibaura-it.ac.jp/~goro/achievement.html

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.mcs.se.shibaura-it.ac.jp/~goro/achievement.html

    • Related Report
      2007 Annual Research Report
  • [Remarks] 平成19年度研究成果として2本の論文を現在投稿中である。

    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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