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Nonlinear hyperbolic-parabolic singular perturbation

Research Project

Project/Area Number 19540199
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionTokyo University of Science

Principal Investigator

YAMAZAKI Taeko  Tokyo University of Science, 理工学部, 教授 (60220315)

Co-Investigator(Kenkyū-buntansha) 松山 登喜夫 (松山 登喜男)  東海大学, 理学部, 教授 (70249712)
小林 隆夫  東京理科大学, 理工学部, 教授 (90178319)
立川 篤  東京理科大学, 理工学部, 教授 (50188257)
牛島 健夫  東京理科大学, 理工学部, 講師 (30339113)
Co-Investigator(Renkei-kenkyūsha) 小林 隆夫  東京理科大学, 理工学部, 教授 (90178319)
立川 篤  東京理科大学, 理工学部, 教授 (50188257)
牛島 健夫  東京理科大学, 理工学部, 准教授 (30339113)
Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords双曲型方程式 / 特異摂動問題 / 消散項 / Kirchhoff方程式 / 解析学 / 関数方程式論 / 非線形解析
Research Abstract

時間に関する2階微分の項がパラメータを係数とする消散項のある双曲型方程式のパラメータを0に近づけると、形式的には放物型方程式となる。臨界べきまたはそれよりも遅く減衰する消散項を持った線形および非線形双曲型方程式と対応する放物型方程式の解との差の時間一様な評価、さらに時間減衰評価を得た。更に、この結果をKircchoff型準線型方程式に応用し、特異摂動問題における時間減衰収束評価を示すと同時に大域解の一意存在も示した。

Report

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

    (23 results)

All 2009 2008 2007 Other

All Journal Article (11 results) (of which Peer Reviewed: 10 results) Presentation (12 results)

  • [Journal Article] Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation2009

    • Author(s)
      Taeko Yamazaki
    • Journal Title

      Math. Methods in Appl. Sci. Mathematical Methods in the Applied Sciences (印刷中)(Published Online)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] L^p-L^q estimates for wave equations and the Kirchhoff equation2008

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Osaka Journal of Mathematics Vol.45, No.2

      Pages: 491-510

    • NAID

      120004846675

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Regularity of minimizers of some variational integrals with discontinuity2008

    • Author(s)
      Maria Alessandra Ragusa and Atsushi Tachikawa
    • Journal Title

      Z. Anal. Anwend Vol.27, No.4

      Pages: 469-482

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] L^p-L^q estimates for wave equations and the Kirchhoff equation2008

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Osaka Journal of Mathematics 45

    • NAID

      120004846675

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity of minimizers of some variational integrals with discontinuity2008

    • Author(s)
      Maria Alessandra Ragusa, Atsushi Tachikawa
    • Journal Title

      Z. Anal. Anwend. 27

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Diffusion phenomenon for abstract wave equations with decaying dissipation, Advanced Studies in Pure Mathematics2007

    • Author(s)
      Taeko Yamazaki
    • Journal Title

      Asymptotic Analysis and Singularities Vol.47, No.1

      Pages: 363-381

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic-parabolic singular perturbations for quasilinear equations of Kirchhoff type2007

    • Author(s)
      Michihiro Hashimoto and Taeko Yamazaki
    • Journal Title

      J. Differential Equations Vol.237

      Pages: 491-525

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Diffusion phenomenon for abstract wave equations with decaying dissipation,2007

    • Author(s)
      Taeko Yamazaki
    • Journal Title

      Advanced Studies in Pure Mathematics, Asymptotic Analysis and Singularities 47-1

      Pages: 363-381

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hyperbolic-parabolic singular perturbations for quasilinear equations of Kirchhoff type2007

    • Author(s)
      Taeko Yamazaki
    • Journal Title

      J. Differential Equations 237

      Pages: 491-525

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dispersion and asymptotic profiles for Kirchhoff equations,2007

    • Author(s)
      T. Matsuyama and M. Ruzhansky
    • Journal Title

      Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics

      Pages: 234-243

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation

    • Author(s)
      Taeko Yamazaki
    • Journal Title

      Mathmatical Methods in the Applied Sciences (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Singular limit problem Singular limit problem for Kirchhoff equation with weak dissipation2008

    • Author(s)
      Taeko Yamazaki
    • Organizer
      Linear and Nonlinear Waves
    • Place of Presentation
      滋賀県立県民交流センター(No.6)
    • Year and Date
      2008-12-10
    • Related Report
      2008 Final Research Report
  • [Presentation] Singular limit problem for Kirchhoff equation with weak dissipation2008

    • Author(s)
      Taeko Yamazaki
    • Organizer
      Linear and Nonlinear Waves, No. 6
    • Place of Presentation
      滋賀県立県民交流センター
    • Year and Date
      2008-12-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Singular limit for Kirchhoff type quasilinear hyperbolic equation with weak dissipation2008

    • Author(s)
      Taeko Yamazaki
    • Organizer
      7th. AIMS Conference
    • Place of Presentation
      The University of Texas, USA
    • Year and Date
      2008-05-19
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Geometrical optics for hyperbolic equations2008

    • Author(s)
      Tokio Matsuyama
    • Organizer
      研究集会"Decay and regularity for solutions of differential equations and dynamical systems"
    • Place of Presentation
      Department of Mathematics and Informatics of the University of Cagliari, Italy
    • Related Report
      2008 Final Research Report
  • [Presentation] Geometrical optics for hyperbolic equations2008

    • Author(s)
      Tokio Matsuyama
    • Organizer
      Decay and regularity for solutions of differential equations and dynamical systems
    • Place of Presentation
      The University of Cagliari, Italy
    • Related Report
      2008 Annual Research Report
  • [Presentation] Scattering for the Kirchhoff equation with nonlinear perturbations2008

    • Author(s)
      松山 登喜夫
    • Organizer
      Function spaces and partial differential equations
    • Place of Presentation
      大阪大学
    • Related Report
      2007 Annual Research Report
  • [Presentation] Singular perturbation for the Kirchhoff equation with decaying dissipation2007

    • Author(s)
      Taeko Yamazaki
    • Organizer
      Symposium on PDE of Tokai University
    • Place of Presentation
      東海大学
    • Year and Date
      2007-10-31
    • Related Report
      2008 Final Research Report 2007 Annual Research Report
  • [Presentation] Kirchhoff 型方程式の特異摂動問題について2007

    • Author(s)
      山崎多恵子
    • Organizer
      研究集会「非線形の諸問題」
    • Place of Presentation
      鹿児島県市町村自治会館
    • Year and Date
      2007-09-27
    • Related Report
      2008 Final Research Report
  • [Presentation] Kirchhoff型方程式の特異摂動問題について2007

    • Author(s)
      山崎 多恵子
    • Organizer
      研究集会「非線形の諸問題」
    • Place of Presentation
      鹿児島県市町村自治会館
    • Year and Date
      2007-09-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] Partial regularity of harmonic maps into Finsler spaces2007

    • Author(s)
      Atushi Tachikawa
    • Organizer
      International Conference 'Variational Problems in Geometry'
    • Place of Presentation
      仙台国際センター
    • Year and Date
      2007-09-19
    • Related Report
      2008 Final Research Report
  • [Presentation] Partial regularity of harmonic maps into Finsler spaces2007

    • Author(s)
      立川 篤
    • Organizer
      International Conference"Variational Problems in Geometry"
    • Place of Presentation
      仙台国際センター
    • Year and Date
      2007-09-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] Dispersion for the Kirchhoff equations2007

    • Author(s)
      松山 登喜夫
    • Organizer
      6th Isaac Congress 2007
    • Place of Presentation
      アンカラ
    • Related Report
      2007 Annual Research Report

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

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