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

• Project/Area Number: 19740072
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Yamaguchi 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: ¥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.

Research Products

• [Journal Article] Generalized energy conservation for wave equations with time-depending coefficients under stabilization properties. Further progress in analysis (2009)
  • Author(s): F. Hirosawa
  • Journal Title: World Sci. Publ., Hackensack, NJ Pages: 444-453
  • Peer Reviewed
• [Journal Article] Generalised energy conservation law for the wave equations with variable propagation speed (2009)
  • Author(s): F. Hirosawa, J. Wirth
  • Journal Title: Journal of Mathematical Analysis and Applications 1 Pages: 56-74
  • Peer Reviewed
• [Journal Article] Generalised energy conservation law for the wave equations with variable propagation speed (2009)
  • Author(s): F.Hirosawa, J.Wirth
  • Journal Title: J.Math.Anal.Appl. 358 Pages: 56-74
  • Peer Reviewed
• [Journal Article] Loss of regularity for p-evolution type models (2008)
  • Author(s): M. Cicognani, F. Hirosawa, M. Reissig
  • Journal Title: Journal of Mathematical Analysis and Applications 1 Pages: 35-58
  • Peer Reviewed
• [Journal Article] The Log-effect for p-evolution type models (2008)
  • Author(s): M. Cicognani, F. Hirosawa, M. Reissig, M
  • Journal Title: Journal of the Mathematical Society of Japan 3 Pages: 819-863
  • NAID: 10024331949
  • Peer Reviewed
• [Journal Article] On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients (2008)
  • Author(s): M. Cicognani, F. Hirosawa
  • Journal Title: Mathematica Scandinavica 2 Pages: 283-304
  • Peer Reviewed
• [Journal Article] C^m-theory of damped wave equations with stabilisation (2008)
  • Author(s): F. Hirosawa, J. Wirth
  • Journal Title: Journal of Mathematical Analysis and Applications 2 Pages: 1022-1035
  • Peer Reviewed
• [Journal Article] C^-m-theory of damped wave equations with stabilisation (2008)
  • Author(s): F. Hirosawa
  • Journal Title: Journal of Mathematical Analysis and Applications 343 Pages: 1022-1035
  • Peer Reviewed
• [Journal Article] On the Gevrey well-posedness for second order strictly hyperbolic Cauchy problems under the influence of the regularity of the coefficients (2008)
  • Author(s): F. Hirosawa
  • Journal Title: Mathematica Scandinavica 102 Pages: 283-304
  • Peer Reviewed
• [Journal Article] The Log-effect for p-evolution type models (2008)
  • Author(s): F. Hirosawa
  • Journal Title: Journal of the Mathematical Society of Japan 60 Pages: 819-863
  • NAID: 10024331949
  • Peer Reviewed
• [Journal Article] Loss of regularity for p-evolution type models (2008)
  • Author(s): F. Hirosawa
  • Journal Title: Journal of Mathematical Analysis and Applications 347 Pages: 35-58
  • Peer Reviewed
• [Journal Article] On the asymptotic behavior of the energy for the wave equations with time depending coefficients (2007)
  • Author(s): F. Hirosawa
  • Journal Title: Mathematische Annalen 4 Pages: 819-839
  • NAID: 40015709707
  • Peer Reviewed
• [Journal Article] On the asymptotic behavior of the energy for the wave eauations with time depending coefficients (2007)
  • Author(s): F.Hirosawa
  • Journal Title: Mathematische Annalen 339 Pages: 49-70
  • Peer Reviewed
• [Presentation] Genaralized energy conservation for Klein-Gordon equations with effective mass terms (2010)
  • 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
• [Presentation] Genaralized energy conservation for Klein-Gordon equations with effective mass terms (2010)
  • 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
• [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
• [Presentation] Energy estimates for wave equations with time dependent propagation speeds of Gevrey class (2009)
  • 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
• [Presentation] Wave equations with time depending propagation speed (2009)
  • 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
• [Presentation] Wave equations with time dependent coefficients (2009)
  • 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
• [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
• [Presentation] Energy estimates for wave equations with time dependent coefficients (2009)
  • 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
• [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
• [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
• [Presentation] Wave equations with time depending propagation speed (2009)
  • Author(s): F. Hirosawa
  • Organizer: 17th ICFIDCAA at Ho Chi Minh City University of Pedagogy
  • Place of Presentation: Ho-Chi-Minh, Vietnam
• [Presentation] Wave equations with time dependent coefficients (2009)
  • Author(s): F. Hirosawa
  • Organizer: 7th ISAAC Congress (Dispersive Equations) at Imperial College London
  • Place of Presentation: London, UK
• [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
• [Presentation] Energy estimates for wave equations with time dependent coefficients (2009)
  • Author(s): 廣澤史彦
  • Organizer: 24th松山キャンプ
  • Place of Presentation: 山口大学
• [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
• [Presentation] Generalized energy conservation law for the wave equations with time dependent propagation speed (2008)
  • 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
• [Presentation] On wave equations with time dependent coefficients of the Gevrey class (2008)
  • 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
• [Presentation] C^m-theory of damped wave equations with stabilization (2008)
  • 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
• [Presentation] C^m-theory of damped wave equations with stabilization (2008)
  • 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
• [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
• [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
• [Presentation] Generalized energy conservation law for the wave equations with time dependent propagation speed (2008)
  • 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
• [Presentation] On wave equations with time dependent coefficients of the Gevrey class (2008)
  • Author(s): F. Hirosawa
  • Organizer: Scientific program of the workshop "Evolution equations" at TU Bergakademie Freiberg
  • Place of Presentation: Freiberg, Germany
• [Presentation] Cm-theory of damped wave equations with stabilization (2008)
  • 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
• [Presentation] Cm-theory of damped wave equations with stabilization (2008)
  • Author(s): F. Hirosawa, J. Wirth
  • Organizer: International Symposium "Function Spaces and Partial Differential Equations" at Osaka University
  • Place of Presentation: Japan
• [Presentation] On the well-posedness for second order weakly hyperbolic cauchy problems under the influences of the regularity of the coefficients (2007)
  • 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
• [Presentation] On the well-posedness for second order weakly hyperbolic cauchy problems under the influences of the regularity of the coefficients (2007)
  • 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
• [Presentation] On the asymptotic behavior of the solutions for second order ordinary differential equations with variable coefficients (2007)
  • 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
• [Presentation] On the well-posedness for second order weakly hyperbolic Cauchy problems under the influences of the regularity of the coefficients (2007)
  • Author(s): F. Hirosawa
  • Organizer: 6th ISAAC Congress (Dispersive Equations) at Middle East Technical University
  • Place of Presentation: Ankara, Turkey
• [Remarks]
  • URL: http://web.cc.yamaguchi-u.ac.jp/~hirosawa/index.htm
• [Remarks]
  • URL: http://web.cc.yamaguchi-u.ac.jp/~hirosawa/index.htm