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Dispersion for the Kirchhoff equation

Research Project

Project/Area Number 21540198
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionChuo University (2011-2013)
Tokai University (2009-2010)

Principal Investigator

MATSUYAMA Tokio  中央大学, 理工学部, 教授 (70249712)

Project Period (FY) 2009-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsKirchhoff 方程式 / 分散型評価 / 外部問題 / キルヒホッフ方程式 / 散乱問題 / 線形双曲型方程式系 / 分散型評価式 / Kirchhoff方程式 / 散逸評価 / 線形偏微分方程式 / 漸近積分 / 一般化されたフーリエ変換 / レゾルベント評価
Research Abstract

In this project we obtained representation formula and dispersive estimates for linear hyperbolic equations via asymptotic integrations method, which was published from C. R. Acad. Sci. Paris and Adv. Differential Equation. There is another result; global existence of solutions for the Kirchhoff equation in exterior domains, and Kirchhoff systems with small data. These results were published from J. Math. Soc. Japan and J. Math. Pures Appl., respectively. Most of this project were done by the joint work with M. Ruzhansky.

Report

(6 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (49 results)

All 2014 2013 2012 2011 2010 2009 Other

All Journal Article (19 results) (of which Peer Reviewed: 19 results) Presentation (28 results) (of which Invited: 5 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Perturbed Besov spaces by a short-range type potential in an exterior domain2014

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Fourier Analysis, Pseudo-Differential Operators, Time-frequency Analysis and Partial Differential Equations, Trends in Math., M. Ruzhansky and V. Turunen eds.、Springer Basel, Birkhause

      Pages: 285-309

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Perturbed Besov spaces by a short-range type potential in an exterior domain2014

    • Author(s)
      T. Matsuyama
    • Journal Title

      Fourier Analysis, Pseudo-Differential Operators, Time-frequency Analysis and Partial Differential Equations, Trends in Math., M. Ruzhansky and V. Turunen eds.、Springer Basel, Birkhauser

      Volume: なし

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering for strictly hyperbolic systems with time-dependent coefficients2013

    • Author(s)
      Tokio Matsuyama and Michael Ruzhansky
    • Journal Title

      Math. Nachr

      Volume: vol. 286, no. 11-12

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness of Kirchhoff systems2013

    • Author(s)
      Tokio Matsuyama and Michael Ruzhansky
    • Journal Title

      J. Math. Pures Appl

      Volume: (9), vol. 100, no. 2

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness of Kirchhoff systems2013

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

      J. Math. Pures Appl.

      Volume: 100 Pages: 220-240

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering for strictly hyperbolic systems with time-dependent coefficients2013

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

      Math. Nachr.

      Volume: 28 Pages: 1191-1207

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness of Kirchhoff systems2013

    • Author(s)
      Tokio Matsuyama and Michael Ruzhansky
    • Journal Title

      J. Math. Pures Appl.

      Volume: - Issue: 2 Pages: 220-240

    • DOI

      10.1016/j.matpur.2012.12.002

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering for strictly hyperbolic systems with time-dependent coefficients2013

    • Author(s)
      Tokio Matsuyama and Michael Ruzhansky
    • Journal Title

      Math. Nachr.

      Volume: - Issue: 11-12 Pages: 1191-1207

    • DOI

      10.1002/mana.201200095

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perturbed Besov spaces by a short-range type potential in an exterior domain2013

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Progress in Math., Birkhauser

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representation formula of the resolvent for wave equation with a potential outside the convex obstacle2012

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Evolution equations of hyperbolic and Schrödinger type, Progress of Math, Birkhäuser/Springer Basel AG, Basel

      Volume: vol. 301

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation2010

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      J. Math. Soc. Japan

      Volume: vol. 62, no. 4

    • NAID

      10027871075

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Kirchhoff equation with global solutions in unbounded domains2010

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Rend. Istit. Mat. Univ. Trieste

      Volume: vol. 42(suppl)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic integration and dispersion for hyperbolic equations2010

    • Author(s)
      Tokio Matsuyama and Michael Ruzhansky
    • Journal Title

      Adv. Differential Equations

      Volume: vol. 15, no. 7-8

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation2010

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      J.Math.Soc.Japan

      Volume: 4 Pages: 1167-1204

    • NAID

      10027871075

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Kirchhoff equation with global solutions in unbounded domains2010

    • Author(s)
      Tokio Matsuyama
    • Journal Title

      Rend.Istit.Mat.Univ.Trieste

      Volume: 42Suppl Pages: 125-141

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic integration and dispersion for hyperbolic equations2010

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

      Advances in Differential Equations 15

      Pages: 721-756

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness for the exterior initial-boundary value problem to the Kirchhoff equation2010

    • Author(s)
      T.Matsuyama
    • Journal Title

      J.Math.Soc. Japan (掲載確定)

    • NAID

      10027871075

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Time decay for hyperbolic equations with homogeneous symbols2009

    • Author(s)
      Tokio Matsuyama and Michael Ruzhansky
    • Journal Title

      C. R. Math. Acad. Sci. Paris

      Volume: vol. 347, no. 15-16

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time decay for hyperbolic equations with homogeneous symbols2009

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

      C.R.Acad. Sci.Paris, Ser. I 347

      Pages: 915-919

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Global existence for Kirchhoff systems Analysis seminar of Imperial College London Department of Mathematics2014

    • Author(s)
      Tokio Matsuyama
    • Organizer
      Imperial College London
    • Related Report
      2013 Final Research Report
  • [Presentation] Global existence for Kirchhoff systems2014

    • Author(s)
      T. Matsuyama
    • Organizer
      Analysis seminar of Imperial College London
    • Place of Presentation
      Department of Mathematics, Imperial College London
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Kirchhoff方程式のGevrey適切性応用解析研究会2013

    • Author(s)
      松山登喜夫
    • Organizer
      早稲田大学理工学術院
    • Related Report
      2013 Final Research Report
  • [Presentation] Well-posedness of the Kirchhoff equation with small data Joint CRM-Isaac Conference on Fourier Analysis and Approximation Theory2013

    • Author(s)
      Tokio Matsuyama
    • Organizer
      Centre de Recerca Matematica, Bellaterra, Barcelona
    • Related Report
      2013 Final Research Report
  • [Presentation] Global well-posedness of the Kirchhoff equation and systems2013

    • Author(s)
      Tokio Matsuyama
    • Organizer
      9th International ISAAC Congress, Plenary speaker
    • Place of Presentation
      Pedagogical University of Krakow, Polland
    • Related Report
      2013 Final Research Report
  • [Presentation] Kirchhoff方程式のGevrey適切性2013

    • Author(s)
      松山登喜夫
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学理工学術院
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Well-posedness of the Kirchhoff equation with small data2013

    • Author(s)
      T. Matsuyama
    • Organizer
      Joint CRM-ISAAC Conference on Fourier Analysis and Approximation Theory
    • Place of Presentation
      Centro di Matematica, Barcelona, Spain
    • Related Report
      2013 Annual Research Report
  • [Presentation] Global well-posedness of the Kirchhoff equation and systems2013

    • Author(s)
      T. Matsuyama
    • Organizer
      9th International ISAAC Congress
    • Place of Presentation
      Pedagogical University of Krakow, Polland
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Strichartz estimates for hyperbolic systems with time-dependent coefficients2012

    • Author(s)
      Tokio Matsuyama
    • Organizer
      International Conference on Fourier Analysis and Pseudo-Differential Operators
    • Place of Presentation
      Aalto University, Helsinki
    • Related Report
      2013 Final Research Report
  • [Presentation] Asymptotic properties for hyperbolic systems with time-dependent coefficients2011

    • Author(s)
      T.Matsuyama
    • Organizer
      8th International ISAAC Congress in Moscow
    • Place of Presentation
      People's Friendship University of Russia
    • Year and Date
      2011-08-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in exterior domains2011

    • Author(s)
      T.Matsuyama
    • Organizer
      Asymptotic Properties of Solutions to Hyperbolic Equations
    • Place of Presentation
      Imperial College London(United Kingdom)
    • Year and Date
      2011-03-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic properties for hyperbolic systems with time-dependent coefficients2011

    • Author(s)
      Tokio Matsuyama
    • Organizer
      8th International ISAAC Congress
    • Place of Presentation
      Moscow People
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in an exterior domain2011

    • Author(s)
      Tokio Matsuyama
    • Organizer
      Asymptotic Properties of Solutions to Hyperbolic Equations
    • Place of Presentation
      Imperial College London
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in exterior domains2010

    • Author(s)
      T.Matsuyama
    • Organizer
      Microlocal Days, Imperial College London
    • Place of Presentation
      Imperial College London(United Kingdom)
    • Year and Date
      2010-12-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in exterior domains2010

    • Author(s)
      T.Matsuyama
    • Organizer
      International Workshop on Global Properties of Partial Differential Equations on Manifolds
    • Place of Presentation
      Department of Mathematics and Informatics of the University of Cagliari (Italy)
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dispersion and Strichartz estimates for wave equation with a potential in exterior domains2010

    • Author(s)
      T.Matsuyama
    • Organizer
      International Workshop Fourier Analysis and Partial Differential Equations
    • Place of Presentation
      University of Goettingen(Germany)
    • Year and Date
      2010-06-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in an exterior domain2010

    • Author(s)
      Tokio Matsuyama
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      京都大学理学研究科
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in an exterior domain2010

    • Author(s)
      Tokio Matsuyama
    • Organizer
      Microlocal Day #2
    • Place of Presentation
      Imperial College London
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion for 3D wave equation with a potential in an exterior domain2010

    • Author(s)
      Tokio Matsuyama
    • Organizer
      超局所解析と偏微分方程式
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispension for 3D wave equation with a potential in exterior domains2010

    • Author(s)
      Tokio Matsuyama
    • Organizer
      International Workshop on Global Properties of Partial Differential Equations on Manifolds
    • Place of Presentation
      Department of Mathematics and Informatics of the University of Cagliari (Italy)
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion and Strichartz estimates for wave equation with a potential in exterior domains2010

    • Author(s)
      Tokio Matsuyama
    • Organizer
      International Workshop "Fourier Analysis and Partial Differential Equations
    • Place of Presentation
      University of Göttingen (Germany)
    • Related Report
      2013 Final Research Report
  • [Presentation] Kirchhoff equation in an exterior domain2009

    • Author(s)
      T.Matsuyama
    • Organizer
      GF2009
    • Place of Presentation
      Wien University
    • Year and Date
      2009-09-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Strichartz estimates for wave equation with a potential in an exterior domain2009

    • Author(s)
      T.Matsuyama
    • Organizer
      ISAAC Congress 2009
    • Place of Presentation
      Imperial College London
    • Year and Date
      2009-06-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] Kirchhoff方程式の外部問題2009

    • Author(s)
      松山登喜夫
    • Organizer
      応用解析研究会500回記念講演会
    • Place of Presentation
      早稲田大学理工学術院
    • Related Report
      2013 Final Research Report
  • [Presentation] Kirchhoff equation in an exterior domain2009

    • Author(s)
      Tokio Matsuyama
    • Organizer
      International Conference on Generalized Functions
    • Place of Presentation
      Wien University (Austria)
    • Related Report
      2013 Final Research Report
  • [Presentation] Strichartz estimates for hyperbolic equations in an exterior domain2009

    • Author(s)
      Tokio Matsuyama
    • Organizer
      7th International ISAAC
    • Place of Presentation
      Congress Imperial College London (United Kingdom)
    • Related Report
      2013 Final Research Report
  • [Presentation] Strichartz estimates for hyperbolic systems with time-dependent coefficients

    • Author(s)
      Tokio Matsuyama
    • Organizer
      Fourier Analysis and Pseudo-Differential Operators
    • Place of Presentation
      Aalto University, Helsinki
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Perturbed Besov spaces by short-range type potential in exterior domains

    • Author(s)
      Tokio Matsuyama
    • Organizer
      調和解析駒場セミナー
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] 数学通信「書評」エリアス・M・スタイン,ラミ・シャカルチ共著、新井仁之・杉本充・高木啓行・千原浩之訳、「フーリエ解析入門」(プリンストン解析学講義I)日本評論社, 2007年,312頁2010

    • Author(s)
      松山登喜夫・望月清
    • Total Pages
      3
    • Publisher
      日本数学会
    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.u-tokai.ac.jp/

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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