Hamilton flows and Partial Differential Equations

• Project/Area Number: 18540158
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: University of Tsukuba
• Principal Investigator: KAJITANI Kunihiko University of Tsukuba, 名誉教授 (00026262)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,150,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥750,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: キルヒホフ方程式 / 波動方程式 / 大域解 / 散乱問題 / 解の減衰 / ノントラッピング条件 / 時間大域解 / ストークス方程式 / L^p評価 / ハミルトン流 / L^評価 / 解の時間減衰 / 波動作用素 / 解の散乱 / 摂動された波動方程式 / 時間減衰 / ジュブレイクラス / ストースク方程式 / ノントラッピンク条件 / 散乱理論

Research Abstract

Under the non-trapping condition we proved that there exist the global solution of the Cauchy problem for Kirchhoff equations and moreover that the wave operator and the scattering operator for perturbed Kirchhoff equations.

Research Products

• [Journal Article] Time global solutions to the Cauchy problem for multidimensional perturbed Kirchhoff equations (2009)
  • Author(s): K. Kajitani
  • Journal Title: Phase Space Analysis of Partial Differential Equations, Edited by Antonio Bove, Springer imprint Birkhauser Boston Pages: 138-149
  • Peer Reviewed
• [Journal Article] Time global solutions to the Cauchy problem for multidimensional perturbed Kirchhoff equations (2009)
  • Author(s): 梶谷邦彦
  • Journal Title: Phase Space Analysis of Partial Differential Equations, Edited by Antonio Bove, Springer imprint Birkhauser Boston Pages: 138-149
  • Peer Reviewed
• [Journal Article] Scattering for multidimensional Kirchhoff equations (2009)
  • Author(s): 梶谷邦彦
  • Journal Title: Jounal of Mathematical Society (投稿中)
  • Peer Reviewed
• [Journal Article] Time global solutions to the Cauchy problem for multidimensional perturbed Kirchoff equations, Phase Space Analysis of Partial Differential Equations (2009)
  • Author(s): 梶谷邦彦
  • Journal Title: Edited by Antonio Bove, Springer imprint Birkhauser Boston Pages: 138-149
  • Peer Reviewed
• [Journal Article] Scattering for one dimensional perturbed Kirchhoff equations (2008)
  • Author(s): K. Kajitani
  • Journal Title: Journal Mathematical Society of Japan vol. 60 Pages: 665-693
  • NAID: 10024331865
  • Peer Reviewed
• [Journal Article] Scattering for one dimensional perturbed Kirhhoff equations (2008)
  • Author(s): 梶谷邦彦
  • Journal Title: Math. Soc. Vol.60, No.3 Pages: 665-694
  • Peer Reviewed
• [Journal Article] Scattering for one dimensional perturbed Kirhhoff equations (2008)
  • Author(s): 梶谷邦彦
  • Journal Title: Journal. Mathematical Society of. Japan. 60 Pages: 665-693
  • Peer Reviewed
• [Journal Article] Scattering for one dimensional perturbed Kirhhoff equations (2008)
  • Author(s): Kunihiko Kajitani
  • Journal Title: Journal of the mathematical society of Japan 60(印刷中)
  • Peer Reviewed
• [Journal Article] Time decay estimates of solutions for wave equations with variable coefficients (2006)
  • Author(s): K. Kajitani
  • Journal Title: Hyperbolic Problem and Regularity questions, Trend in Mathematics, Birkhauser, Verlag Basel/Switzerland Pages: 121-138
  • Peer Reviewed
• [Journal Article] On the existence in Gevrey classes of local solutions to the Cauchy problem nonlinear hyperbolic systems with Holder continuous coefficients (2006)
  • Author(s): K. Kajitani, Yuzawa
  • Journal Title: Annali dell'Universita di Ferrara 55 Pages: 303-315
  • Peer Reviewed
• [Journal Article] The Cauchy problem for hyperbolic systems with Holder contiuous coefficients with respect to the time variables (2006)
  • Author(s): K. Kajitani, Yuzawa
  • Journal Title: Ann.Scuola Norm.Sup.Pisa Cl.Sci. vol. V Pages: 465-482
  • Peer Reviewed
• [Journal Article] Time decay estimates of solutions for wave equations with variable coefficients (2006)
  • Author(s): 梶谷邦彦
  • Journal Title: Hyperbolic Problem and Regularity questions Trends in Mathematics (Birkhauser) Pages: 121-138
  • Peer Reviewed
• [Journal Article] On the existence in Gevrey classes of local solutions to the Cauchy Problem for nonlinear hyperbolic systems with Holder continuous coefficients (2006)
  • Author(s): K.Kajitani, Y.Uzawa
  • Journal Title: Annali dell' Universita di Ferrara 52 Pages: 303-315
• [Journal Article] The Cauchy problem for hyperbolic systems with Holder continuous coefficients with respect to the time variable (2006)
  • Author(s): K.Kajitani, Y.Uzawa
  • Journal Title: Annali della Scuola Normale Suyperiore di Pisa, Classe di Scienze Serie 5 5 Pages: 465-482
• [Journal Article] Time decay estimates of solutions for wave equations with variable coefficients (2006)
  • Author(s): K.Kajitani
  • Journal Title: Hyperbolic Problems and Regularity Questions, Trends in Mathematics, Ed. M. Padula ＆ L. Zanghirati, birkhauser Verlag Basel/Switzerland Pages: 121-136
• [Presentation] L^p estimates of solutions of mixed problem for heat equations (2010)
  • Author(s): K. Kajitani
  • Organizer: 東海大学シンポジウム
  • Place of Presentation: 東海大学(招待講演)
  • Year and Date: 2010-03-11
• [Presentation] L^p estimates of solutions of mixed problem for heat equations (2009)
  • Author(s): K. Kajitani
  • Organizer: ポアンカレ研究所解析セミナー
  • Place of Presentation: フランス パリ(招待講演)
  • Year and Date: 2009-12-18
• [Presentation] Decay estimates of solutions of mixed problem for heat equation in a Half space (2009)
  • Author(s): 梶谷邦彦
  • Organizer: パリ第6大学解析セミナー
  • Place of Presentation: フランス パリポアンカレ研究所
  • Year and Date: 2009-12-18
• [Presentation] Mixed problem for Stokes equations (2009)
  • Author(s): K. Kajitani
  • Organizer: 東海大学シンポジウム
  • Place of Presentation: 東海大学(招待講演)
  • Year and Date: 2009-03-10
• [Presentation] ストークス方程式に対する混合問題 (2009)
  • Author(s): 梶谷邦彦
  • Organizer: 早稲田応用解析シンポシウム
  • Place of Presentation: 熱海
  • Year and Date: 2009-03-03
• [Presentation] ストークス方程式に対する混合問題の会の評価 (2009)
  • Author(s): 梶谷邦彦
  • Organizer: 東海大学解析学シンポジウム
  • Place of Presentation: 東海大学
  • Year and Date: 2009-03-01
• [Presentation] Scattering for multidimensional Kirchhoff equations (2008)
  • Author(s): K. Kajitani
  • Organizer: ポアンカレ研究所解析セミナー
  • Place of Presentation: フランス パリ(招待講演)
  • Year and Date: 2008-12-17
• [Presentation] Scattering for multidimensional Kirchohh equations (2008)
  • Author(s): 梶谷邦彦
  • Organizer: Poincare Seminaire
  • Place of Presentation: フランス パリ ポアンカレ研究所
  • Year and Date: 2008-12-17
• [Presentation] Scattering for perturbed Kirchhoff equations (2008)
  • Author(s): K. Kajitani
  • Organizer: 東海大学シンポジウム
  • Place of Presentation: 東海大学(招待講演)
  • Year and Date: 2008-11-01
• [Presentation] キルヒホフ方程式に対する初期値問題の時間大域解 (2008)
  • Author(s): 梶谷邦彦
  • Organizer: 東海大学解析学シンポジウム
  • Place of Presentation: 東海大学
  • Year and Date: 2008-11-01
• [Presentation] Scattering for Kirchohh type equations (2008)
  • Author(s): 梶谷邦彦
  • Organizer: Sumposium of P.D.E.,of Univ. of Cagriali
  • Place of Presentation: イタリア カリアリ大学
  • Year and Date: 2008-09-24
• [Presentation] Time global solutions of Kirchhoff equations (2008)
  • Author(s): K. Kajitani
  • Organizer: トリエステ大学解析セミナー
  • Place of Presentation: イタリア, トリエステ(招待講演)
  • Year and Date: 2008-09-18
• [Presentation] Time global solutions to the Cauchy problem for Kirchohh equations (2008)
  • Author(s): 梶谷邦彦
  • Organizer: Seminar of Analysis of Univ. of Trieste
  • Place of Presentation: イタリア トリエステ大学
  • Year and Date: 2008-09-18
• [Presentation] Time global solutions to the Cauchy problem for perturbed Kirchhoff equations (2007)
  • Author(s): K. Kajitani
  • Organizer: ポアンカレ研究所解析セミナー
  • Place of Presentation: フランス パリ(招待講演)
  • Year and Date: 2007-12-19
• [Presentation] 多次元キルヒホフ方程式初期値問題の時間大域解 (2007)
  • Author(s): K. Kajitani
  • Organizer: 稲田大応用解析セミナー
  • Place of Presentation: 早稲田大学(招待講演)
  • Year and Date: 2007-12-07
• [Presentation] Time global solutions to the Cauchy problem for perturbed Kirchhoff equations (2007)
  • Author(s): K. Kajitani
  • Organizer: シエナ大学シンポジウム
  • Place of Presentation: イタリア, シエナ(招待講演)
  • Year and Date: 2007-10-12
• [Presentation] Time global solutions to the Cauchy problem for Kirhhoff equations (2007)
  • Author(s): 梶谷 邦彦
  • Organizer: Pfase space analysis of PDEs
  • Place of Presentation: イタリア シエナ大学
  • Year and Date: 2007-10-12
• [Presentation] Scattering theory for one dimensional perturbed Kirchhoff (2007)
  • Author(s): K. Kajitani
  • Organizer: 東海大学シンポジウム
  • Place of Presentation: 東海大学(招待講演)
  • Year and Date: 2007-03-09
• [Presentation] The Cauchy problem for one dimensional Kirchhoff equations (2006)
  • Author(s): K. Kajitani
  • Organizer: ポアンカレ研究所解析セミナー
  • Place of Presentation: ランス パリ(招待講演)
  • Year and Date: 2006-12-13
• [Presentation] The global solutions of the Cauchy problem for one dimensional perturbed Kichhoff equations (2006)
  • Author(s): K. Kajitani
  • Organizer: 東海大学シンポジウム
  • Place of Presentation: 東海大学(招待講演)
  • Year and Date: 2006-10-29
• [Presentation] Scattering for one dimensional Kirchhoff equations (2006)
  • Author(s): K. Kajitani
  • Organizer: ピサ大学解析セミナー
  • Place of Presentation: イタリア, ピサ(招待講演)
  • Year and Date: 2006-09-08