real/complex analytic functions and theory of nonlinear partial differential equations

• Project/Area Number: 17540182
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kwansei Gakuin University
• Principal Investigator: YAMANE Hideshi Kwansei Gakuin University, 理工学部, 教授 (80286145)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,140,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2007: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2006: ¥500,000 (Direct Cost: ¥500,000); Fiscal Year 2005: ¥600,000 (Direct Cost: ¥600,000)
• Keywords: 非線型方程式 / 実解析関数 / 複素解析関数 / フックス型 / 特異解 / 偏微分方程式 / 非線形シュレーディンガー方程式 / 非線型偏微分方程式 / フックス型偏微分方程式 / Fuchsian Reduction / 熱方程式 / 逆問題 / 非線形偏微分方程式

Research Abstract

関数論(複素解析)の手法を使って非線型偏微分方程式について調べた.ある曲面または曲線に沿って特異性をもつ解を構成することに興味がある.非線型波動方程式を始めとするある種の非線型偏微分方程式については主要項が対数関数で表される特異解を構成した.非線型シュレーディンガー方程式について,主要項が-1乗の特異性を持つ形式解の収束を証明した.

Research Products

• [Journal Article] 熱方程式の逆問題-春木・磯論文(8巻1号)の条件の緩和について (2008)
  • Author(s): 山根英司
  • Journal Title: 日本応用数理学会論文誌 18(2) Pages: 267-270
  • NAID: 110006793757
  • Peer Reviewed
• [Journal Article] Logarithmic singularities of solutions to nonlinear partial differential equations (2008)
  • Author(s): Hideshi YAMANE, Hidetoshi Tahara
  • Journal Title: Journal of the Mathematical Society of Japan 60(2) Pages: 603-630
  • NAID: 10024331825
  • Peer Reviewed
• [Journal Article] Nonlinear wave equations and Fuchsian equations (2008)
  • Author(s): Hideshi Yamane
  • Journal Title: RIMS Kokyuroku Bessatsu B5 Pages: 1-6
  • Peer Reviewed
• [Journal Article] Nonlinear wave equations and singular solutions (2008)
  • Author(s): Hideshi Yamane
  • Journal Title: Proceedings of the American Mathematical Society 135,no.11 Pages: 3659-3667
  • Peer Reviewed
• [Journal Article] Nonlinear wave equations and singular solutions (2007)
  • Author(s): Hideshi YAMANE
  • Journal Title: Proceedings of the American Mathematical Society 135(11) Pages: 3659-3667
  • Peer Reviewed
• [Journal Article] Nonlinear Cauchy problems with small analytic data (2006)
  • Author(s): Hideshi YAMANE
  • Journal Title: Proceedings of the American Mathematical Society 134(11) Pages: 3353-3361
  • Peer Reviewed
• [Journal Article] Nonlinear Cauchy problems with small analytic data (2006)
  • Author(s): Yamane, Hideshi
  • Journal Title: Proceedings of the American Mathematical Society 134,no.11 Pages: 3353-3361
• [Presentation] 非線型偏微分方程式と動く特異性 (2008)
  • Author(s): 山根英司
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 京都大学理学部
  • Year and Date: 2008-12-21
• [Presentation] Decay and regularity for solutions of differential equations and dynamical systems (2008)
  • Author(s): Hideshi YAMANE
  • Organizer: Logarithmic singularities of solutions to nonlinear partial differential equations
  • Place of Presentation: Universita' di Cagliari(イタリア)
  • Year and Date: 2008-09-24
• [Presentation] 解析的な方程式の新しい取り組み-変換論と特異解、Stokes問題-(New approach to analytic equations-transformation theory, singular solutions and Stokes problem-) (2008)
  • Author(s): Hideshi YAMANE
  • Organizer: Logarithmic singularities of solutions to nonlinear partial differential equations
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-09-18
• [Presentation] The Institute of Mathematics of the Polish Academy of Science (2008)
  • Author(s): Hideshi YAMANE
  • Organizer: Logarithmic singularities of solutions to nonlinear partial differential equations(The Banach Center Conference, Formal and Analytic Solutions of Differential Equations)
  • Place of Presentation: Bedlewo,ポーランド
  • Year and Date: 2008-08-14
• [Presentation] 非線型偏微分方程式の解が持つ対数的特異性 (2008)
  • Author(s): 山根英司
  • Organizer: 日本数学会
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-25
• [Presentation] Singular solutions to nonlinear PDEs : a Fuchsian approach (2007)
  • Author(s): 山根英司
  • Organizer: 数学統計学院主催のセミナー
  • Place of Presentation: 武漢大学, 中国
  • Year and Date: 2007-03-07
• [Presentation] 微分方程式系の代数解析と完全WKB解析 (2006)
  • Author(s): 山根英司
  • Organizer: Nonlinear wave equations and singular solutions
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2006-12-11
• [Presentation] Partial differential equations on noncompact and singular manifolds (2006)
  • Author(s): 山根英司
  • Organizer: Nonlinear wave equations and singular solutions
  • Place of Presentation: Potsdam University,ドイツ
  • Year and Date: 2006-08-09
• [Presentation] 小さい実解析的初期値をもつ非線型コ-シー問題 (2006)
  • Author(s): 山根英司
  • Organizer: 日本数学会
  • Place of Presentation: 中央大学理工学部
  • Year and Date: 2006-03-26
• [Presentation] Partial Differential Equations and Perturbation Analysis (2005)
  • Author(s): 山根英司
  • Organizer: Nonlinear Cauchy Problems with Small Analytic Data
  • Place of Presentation: 武漢大学
  • Year and Date: 2005-09-15
• [Presentation] 漸近解析と特異性 (2005)
  • Author(s): 山根英司
  • Organizer: Nonlinear Cauchy Problems with Small Analytic Data, 日本数学会国際研究集会
  • Place of Presentation: 仙台国際センター
  • Year and Date: 2005-07-19
• [Book] 関数とはなんだろう (2008)
  • Author(s): 山根英司
  • Total Pages: 238
  • Publisher: 講談社ブルーバックス
• [Book] 関数とはなんだろう (2008)
  • Author(s): 山根英司
  • Total Pages: 238
  • Publisher: 講談社
• [Remarks]
  • URL: http://sci-tech.ksc.kwansei.ac.jp/~yamane/
• [Remarks]
  • URL: http://sci-tech.ksc.kwansei.ac.jp/~yamane/
• [Remarks]
  • URL: http://sci-tech.ksc.kwansei.ac.jp/~yamane/