Analysis of nonlinear partial differential equation of wave phenomenon or plasma phenomenon

• Project/Area Number: 17540162
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: The University of Tokushima
• Principal Investigator: ONO Kosuke The University of Tokushima, 総合科学部, 准教授 (00263806)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,780,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥480,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 関数方程式 / dissipative wave / sublinear equation / exterior problem / L^1 estimate

Research Abstract

自然現象の多くは偏微分方程式として数式で記述され解析されていて, 波動現象が摩擦の影響を受けている場合の解析には消散型波動方程式の解構造の研究が必要となる. 本研究では一般奇数次元の全空間におけるコーシー問題に対する消散型波動方程式の解のL^1ノルムの一様有界性の証明やL^p タイプの減衰評価式の厳密な解析を行った. また, 4次元と5次元の場合には自己相互作用の非線形項をもつ非線形消散型波動方程式の時間大域解の一意存在定理の証明やエネルギー評価式の厳密な解析を行った. さらに, 外部領域における初期値境界値問題に対する消散型波動方程式の解空間構造の研究をおこなった.

Research Products

• [Journal Article] Existence of global and bounded solutions for damped sublinear wave equations (2008)
  • Author(s): Kosuke Ono
  • Journal Title: Journal of Mathematics, The University of Tokushima Vol.42 Pages: 19-26
  • NAID: 110007127171
• [Journal Article] Existence of global and bounded solutions for damped sublinear wave equations (2008)
  • Author(s): 小野公輔
  • Journal Title: Journal of Mathematics, The University of Tokushima 42 Pages: 19-26
  • NAID: 110007127171
• [Journal Article] L^1 estimates for dissipative wave equations in exterior domains (2007)
  • Author(s): Kosuke Ono
  • Journal Title: Journal of Mathematical Analysis and Applications Vol.333 No.2 Pages: 1079-1092
  • Peer Reviewed
• [Journal Article] L^1 estimates for the dissipative wave equation in a two dimensional exterior domain (2007)
  • Author(s): Kosuke Ono
  • Journal Title: Journal of Mathematics, The University of Tokushima Vol.41 Pages: 43-57
  • NAID: 110006853406
• [Journal Article] L^1 estimates for dissipative wave equations in exterior domains (2007)
  • Author(s): 小野 公輔
  • Journal Title: Journal of Mathematical Analysis and Applications 333 Pages: 1079-1092
  • Peer Reviewed
• [Journal Article] L^1 estimates for the dissipative wave equation in a two dimensional exterior domain (2007)
  • Author(s): 小野 公輔
  • Journal Title: Journal of Mathematics, The University of Tokushima 41 Pages: 43-57
  • NAID: 110006853406
• [Journal Article] Global solvability for the semilinear damped wave equations in Four and Five Dimensions (2006)
  • Author(s): Kosuke Ono
  • Journal Title: Funkcialaj Ekvacioj Vol.49 No.2 Pages: 215-233
  • Peer Reviewed
• [Journal Article] Global solvability for the semilinear damped wave equations in Four and Five Dimensions (2006)
  • Author(s): 小野公輔
  • Journal Title: Funkcialaj Ekvacioj 49・2 Pages: 215-233
• [Journal Article] L^p decay problem for the dissipative wave equation in odd dimensions (2005)
  • Author(s): Kosuke Ono
  • Journal Title: Journal of Mathematical Analysis and Applications Vol.310 No.2 Pages: 347-361
  • Peer Reviewed
• [Journal Article] On L^1 estimates for solutions of dissipative wave equations (2005)
  • Author(s): Kosuke Ono
  • Journal Title: Nonlinear Analysis Vol.63 No.5-7 Pages: 1769-1777
  • Peer Reviewed
• [Journal Article] L^p decay problem for the dissipative wave equation in odd dimensions (2005)
  • Author(s): 小野公輔
  • Journal Title: Journal of Mathematical Analysis and Applications 310・2 Pages: 347-361
• [Journal Article] On L^1 estimates for solutions of dissipative wave equations (2005)
  • Author(s): 小野公輔
  • Journal Title: Nonlinear Analysis 67・5-7 Pages: 1769-1777
• [Presentation] 外部領域における dissipative wave equation の解の L^1 評価について (2006)
  • Author(s): 小野公輔
  • Organizer: 早稲田大学理工学部講演会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2006-11-17
• [Presentation] L^1 estimates for dissipative wave equations in an exterior domain (2006)
  • Author(s): 小野公輔
  • Organizer: 偏微分方程式特別研究集会, A Special Conference on Partial Differential Equations
  • Place of Presentation: 福岡大学セミナーハウス
  • Year and Date: 2006-10-27
• [Presentation] On L^1 estimates for dissipative wave equations in exterior domains (2005)
  • Author(s): 小野公輔
  • Organizer: 2005年度日本数学会秋期総合分科会
  • Place of Presentation: 岡山大学
  • Year and Date: 2005-09-21
• [Book] 初歩からの複素解析 (2007)
  • Author(s): 香田温人・小野公輔(共著)
  • Total Pages: 140
  • Publisher: 学術図書出版社, 第1版第2刷
• [Book] 理工系の線形代数学入門 (2005)
  • Author(s): 守安一峰・小野公輔(共著)
  • Total Pages: 185
  • Publisher: サイエンス社, 初版第2刷
• [Book] 理工系の線形代数学入門(初版第2刷発行) (2005)
  • Author(s): 守安一峰, 小野公輔
  • Total Pages: 185
  • Publisher: サイエンス社