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On the asymptotic analysis of partial differential equations with variable coefficients and their applications

Research Project

Project/Area Number 19740072
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionYamaguchi University

Principal Investigator

HIROSAWA Fumihiko  Yamaguchi University, 大学院・理工学研究科, 准教授 (50364732)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,240,000 (Direct Cost: ¥2,700,000、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: ¥900,000 (Direct Cost: ¥900,000)
Keywordsエネルギー保存則 / エネルギー減衰評価 / 変数係数 / 波動方程式 / 消散型波動方程式 / 発展方程式 / エネルギー評価
Research Abstract

We studied the asymptotic behavior of the solution to the Cauchy problems of hyperbolic partial differential equations with variable coefficients. In this research we succeeded to improve the energy estimates for wave equations and dissipative wave equations by applying a new method to construct the asymptotic solutions taking account of the smoothness of the coefficients.

Report

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

    (44 results)

All 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (29 results) Remarks (2 results)

  • [Journal Article] Generalized energy conservation for wave equations with time-depending coefficients under stabilization properties. Further progress in analysis2009

    • Author(s)
      F. Hirosawa
    • Journal Title

      World Sci. Publ., Hackensack, NJ

      Pages: 444-453

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalised energy conservation law for the wave equations with variable propagation speed2009

    • Author(s)
      F. Hirosawa, J. Wirth
    • Journal Title

      Journal of Mathematical Analysis and Applications 1

      Pages: 56-74

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalised energy conservation law for the wave equations with variable propagation speed2009

    • Author(s)
      F.Hirosawa, J.Wirth
    • Journal Title

      J.Math.Anal.Appl. 358

      Pages: 56-74

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Loss of regularity for p-evolution type models2008

    • Author(s)
      M. Cicognani, F. Hirosawa, M. Reissig
    • Journal Title

      Journal of Mathematical Analysis and Applications 1

      Pages: 35-58

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Log-effect for p-evolution type models2008

    • Author(s)
      M. Cicognani, F. Hirosawa, M. Reissig, M
    • Journal Title

      Journal of the Mathematical Society of Japan 3

      Pages: 819-863

    • NAID

      10024331949

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients2008

    • Author(s)
      M. Cicognani, F. Hirosawa
    • Journal Title

      Mathematica Scandinavica 2

      Pages: 283-304

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] C^m-theory of damped wave equations with stabilisation2008

    • Author(s)
      F. Hirosawa, J. Wirth
    • Journal Title

      Journal of Mathematical Analysis and Applications 2

      Pages: 1022-1035

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] C^-m-theory of damped wave equations with stabilisation2008

    • Author(s)
      F. Hirosawa
    • Journal Title

      Journal of Mathematical Analysis and Applications 343

      Pages: 1022-1035

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients2008

    • Author(s)
      F. Hirosawa
    • Journal Title

      Mathematica Scandinavica 102

      Pages: 283-304

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Log-effect for p-evolution type models2008

    • Author(s)
      F. Hirosawa
    • Journal Title

      Journal of the Mathematical Society of Japan 60

      Pages: 819-863

    • NAID

      10024331949

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Loss of regularity for p-evolution type models2008

    • Author(s)
      F. Hirosawa
    • Journal Title

      Journal of Mathematical Analysis and Applications 347

      Pages: 35-58

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the asymptotic behavior of the energy for the wave equations with time depending coefficients2007

    • Author(s)
      F. Hirosawa
    • Journal Title

      Mathematische Annalen 4

      Pages: 819-839

    • NAID

      40015709707

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the asymptotic behavior of the energy for the wave eauations with time depending coefficients2007

    • Author(s)
      F.Hirosawa
    • Journal Title

      Mathematische Annalen 339

      Pages: 49-70

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Genaralized energy conservation for Klein-Gordon equations with effective mass terms2010

    • Author(s)
      廣澤史彦
    • Organizer
      発展方程式シンポジウム
    • Place of Presentation
      神奈川(東海大学)
    • Year and Date
      2010-03-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] Genaralized energy conservation for Klein-Gordon equations with effective mass terms2010

    • Author(s)
      廣澤史彦, C. Bohme
    • Organizer
      発展方程式シンポジウム, 東海大学理学部
    • Related Report
      2009 Final Research Report
  • [Presentation] Gevrey classの係数を持つKlein-Gordon型方程式のエネルギー評価2010

    • Author(s)
      廣澤史彦, C. Bohme
    • Organizer
      松山キャンプ
    • Place of Presentation
      愛媛県総合社会福祉会館
    • Related Report
      2009 Final Research Report
  • [Presentation] Energy estimates for wave equations with time dependent propagation speeds of Gevrey class2009

    • Author(s)
      廣澤史彦
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京(東京大学)
    • Year and Date
      2009-12-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Wave equations with time depending propagation speed2009

    • Author(s)
      F.Hirosawa
    • Organizer
      17th ICFIDCAA
    • Place of Presentation
      ホーチミン(ベトナム)
    • Year and Date
      2009-08-06
    • Related Report
      2009 Annual Research Report
  • [Presentation] Wave equations with time dependent coefficients2009

    • Author(s)
      F.Hirosawa
    • Organizer
      7th ISAAC Congress
    • Place of Presentation
      ロンドン(イギリス)
    • Year and Date
      2009-07-17
    • Related Report
      2009 Annual Research Report
  • [Presentation] 変数係数波動方程式の解の安定性について2009

    • Author(s)
      廣澤史彦
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Energy estimates for wave equations with time dependent coefficients2009

    • Author(s)
      F. Hirosawa
    • Organizer
      第24回松山キャンプ
    • Place of Presentation
      山口
    • Year and Date
      2009-01-15
    • Related Report
      2008 Annual Research Report
  • [Presentation] "Energy estimates for wave equations with time dependent propagation speeds of Gevrey class", 微分方程式の総合的研究2009

    • Author(s)
      廣澤史彦
    • Place of Presentation
      東京大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Kirchhoff方程式と変係数波動方程式2009

    • Author(s)
      廣澤史彦
    • Organizer
      八王子偏微分方程式研究集会
    • Place of Presentation
      八王子セミナーハウス
    • Related Report
      2009 Final Research Report
  • [Presentation] Wave equations with time depending propagation speed2009

    • Author(s)
      F. Hirosawa
    • Organizer
      17th ICFIDCAA at Ho Chi Minh City University of Pedagogy
    • Place of Presentation
      Ho-Chi-Minh, Vietnam
    • Related Report
      2009 Final Research Report
  • [Presentation] Wave equations with time dependent coefficients2009

    • Author(s)
      F. Hirosawa
    • Organizer
      7th ISAAC Congress (Dispersive Equations) at Imperial College London
    • Place of Presentation
      London, UK
    • Related Report
      2009 Final Research Report
  • [Presentation] 変数係数波動方程式の解の安定性について2009

    • Author(s)
      廣澤史彦
    • Organizer
      日本数学会2009年度年会, 関数解析学分科会
    • Place of Presentation
      東京大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Energy estimates for wave equations with time dependent coefficients2009

    • Author(s)
      廣澤史彦
    • Organizer
      24th松山キャンプ
    • Place of Presentation
      山口大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Gevrey classの係数を持つ波動方程式のエネルギー評価について2008

    • Author(s)
      廣澤史彦
    • Organizer
      米子偏微分方程式研究集会
    • Place of Presentation
      鳥取
    • Year and Date
      2008-10-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Generalized energy conservation law for the wave equations with time dependent propagation speed2008

    • Author(s)
      廣澤史彦
    • Organizer
      広島微分方程式研究集会
    • Place of Presentation
      広島
    • Year and Date
      2008-10-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] On wave equations with time dependent coefficients of the Gevrey class2008

    • Author(s)
      F. Hirosawa
    • Organizer
      Scientific program of the workshop Evolution equations
    • Place of Presentation
      フライベルグ(ドイツ)
    • Year and Date
      2008-10-01
    • Related Report
      2008 Annual Research Report
  • [Presentation] C^m-theory of damped wave equations with stabilization2008

    • Author(s)
      廣澤 史彦
    • Organizer
      日本数学会年会・函数方程式論分科会
    • Place of Presentation
      大阪
    • Year and Date
      2008-03-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] C^m-theory of damped wave equations with stabilization2008

    • Author(s)
      廣澤 史彦
    • Organizer
      International Symposium "Function Spaces and Partial Differential Equations"
    • Place of Presentation
      大阪
    • Year and Date
      2008-02-20
    • Related Report
      2007 Annual Research Report
  • [Presentation] 振動する消散項を持つ波動方程式のエネルギー減衰について2008

    • Author(s)
      廣澤 史彦
    • Organizer
      松山キャンプ
    • Place of Presentation
      山口
    • Year and Date
      2008-01-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] Gevrey classの係数を持つ波動方程式のエネルギー評価について2008

    • Author(s)
      廣澤史彦
    • Organizer
      米子偏微分方程式研究集会
    • Place of Presentation
      米子高専
    • Related Report
      2009 Final Research Report
  • [Presentation] Generalized energy conservation law for the wave equations with time dependent propagation speed2008

    • Author(s)
      廣澤史彦
    • Organizer
      広島微分方程式研究集会
    • Place of Presentation
      広島大学
    • Related Report
      2009 Final Research Report
  • [Presentation] On wave equations with time dependent coefficients of the Gevrey class2008

    • Author(s)
      F. Hirosawa
    • Organizer
      Scientific program of the workshop "Evolution equations" at TU Bergakademie Freiberg
    • Place of Presentation
      Freiberg, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] Cm-theory of damped wave equations with stabilization2008

    • Author(s)
      廣澤史彦, J. Wirth
    • Organizer
      日本数学会2008年度年会函数方程式論分科会
    • Place of Presentation
      近畿大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Cm-theory of damped wave equations with stabilization2008

    • Author(s)
      F. Hirosawa, J. Wirth
    • Organizer
      International Symposium "Function Spaces and Partial Differential Equations" at Osaka University
    • Place of Presentation
      Japan
    • Related Report
      2009 Final Research Report
  • [Presentation] On the well-posedness for second order weakly hyperbolic cauchy problems under the influences of the regularity of the coefficients2007

    • Author(s)
      F.Hirosawa
    • Organizer
      山中湖偏微分方程式研究集会
    • Place of Presentation
      山梨
    • Year and Date
      2007-10-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the well-posedness for second order weakly hyperbolic cauchy problems under the influences of the regularity of the coefficients2007

    • Author(s)
      F.Hirosawa
    • Organizer
      6'th International Society for Analysis, its AppUcation and Computation
    • Place of Presentation
      アンカラ(トルコ共和国)
    • Year and Date
      2007-08-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the asymptotic behavior of the solutions for second order ordinary differential equations with variable coefficients2007

    • Author(s)
      廣澤史彦
    • Organizer
      山中湖偏微分方程式研究集会
    • Place of Presentation
      東海大学山中湖セミナーハウス
    • Related Report
      2009 Final Research Report
  • [Presentation] On the well-posedness for second order weakly hyperbolic Cauchy problems under the influences of the regularity of the coefficients2007

    • Author(s)
      F. Hirosawa
    • Organizer
      6th ISAAC Congress (Dispersive Equations) at Middle East Technical University
    • Place of Presentation
      Ankara, Turkey
    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://web.cc.yamaguchi-u.ac.jp/~hirosawa/index.htm

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://web.cc.yamaguchi-u.ac.jp/~hirosawa/index.htm

    • Related Report
      2009 Annual Research Report

URL: 

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

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