Diffusion and Geometry of Domain

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20340031
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tohoku University (2012); Hiroshima University (2008-2011)
• Principal Investigator: SAKAGUCHI Shigeru Hiroshima University, 大学院・工学研究院, 教授 (50215620)
• Project Period (FY): 2008 – 2012
• Keywords: 拡散 / 非線形拡散 / 領域の幾何 / 放物型方程式 / 楕円型方程式 / 解の挙動 / 不変な等位面 / 距離関数

Research Abstract

主な研究日的は拡散現象を記述する偏微分方程式の解の挙動と領域の幾何の関係を明らかにすることであり,次の課題について研究する
(1)拡散方程式の解の初期挙動と領域の幾何(境界の曲率や境界からの距離関数)の関係を明らかにする
(2)拡散方程式の解の不変な空間臨界点及び不変な等位面の研究を発展させる
(3)広く拡散現象を考慮した偏微分方程式(楕円型および放物型方程式等)の解の挙動と領域の幾何の関係を調べる
(4)解や領域の形状を決定する逆問題を発掘・設定し,研究する

Research Products

• [Journal Article] A Liouville-type theorem for some Weingarten hypersurfaces (2011)
  • Author(s): Shigeru Sakaguchi
  • Journal Title: Discrete and Continuous Dynamical Systems-Series S 4 Pages: 887-895
  • Peer Reviewed
• [Journal Article] Nonlinear diffusion with a bounded stationary level surface (2010)
  • Author(s): Rolando Magnanini Shigeru Sakaguchi
  • Journal Title: Annales de l'Inst. Henri Poincare (C) Analyse Non Lineaire 27 Pages: 937-952
  • Peer Reviewed
• [Journal Article] Stationary isothermic surfaces and some characterizations of the hyperplane in the N-dimensional Euclidean space (2010)
  • Author(s): Rolando Magnanini Shigeru Sakaguchi
  • Journal Title: J. Differential Equations 248 Pages: 1112-1119
  • Peer Reviewed
• [Presentation] 非線形拡散と領域の幾何 (2010)
  • Author(s): 坂口茂
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-23
• [Presentation] Nonlinear diffusion and geometry of domain (2010)
  • Author(s): Shigeru Sakaguchi
  • Organizer: The 8^<th> AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: ドイツ・ドレスデン工科大学
  • Year and Date: 2010-05-27
• [Presentation] Nonlinear diffusion and geometry of domain (2009)
  • Author(s): Shigeru Sakaguchi
  • Organizer: RIMS研究集会「現象解析と関数方程式の新展望」
  • Place of Presentation: 京都大学
  • Year and Date: 2009-11-19
• [Presentation] A Liouville-type theorem for some Weingarten hypersurfaces (2009)
  • Author(s): Shigeru Sakaguchi
  • Organizer: 1^<st> Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
  • Place of Presentation: 東北大学
  • Year and Date: 2009-06-17
• [Presentation] Diffusion and stationary level surfaces (2008)
  • Author(s): Shigeru Sakaguchi
  • Organizer: 第5回世界非線形解析学者会議(WCNA 2008)
  • Place of Presentation: 米国・オーランド
  • Year and Date: 2008-07-05
• [Presentation] Stationary isothermic surfaces and some characterizations of the hyperplane (2008)
  • Author(s): Shigeru Sakaguchi
  • Organizer: RIMS研究集会「微分方程式の粘性解とその周辺」
  • Place of Presentation: 京都大学
  • Year and Date: 2008-06-25