Diffusion phenomena of solutions for the damped wave equation

2010 Fiscal Year Self-evaluation Report

• Project/Area Number: 20540219
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Waseda University
• Principal Investigator: NISHIHARA Kenji Waseda University, 政治経済学術院, 教授 (60141876)
• Project Period (FY): 2008 – 2012
• Keywords: 関数方程式の大域理論

Research Abstract

研究目的は粘性保存則の非線形波の安定性の研究から派生して、消散型波動方程式の解の拡散現象を観察することである。5年間の研究計画のうち、前半では、
(1)涌き出し項として働く半線形項を持つ半線型消散型波動方程式のコーシー問題、
(2)吸収項として働く半線形項を持つ半線型消散型波動方程式のコーシー問題、
(3)データが必ずしも可積分とは限らない場合の問題、
について、それらの解の挙動を調べることが研究計画の概要である。

Research Products

• [Journal Article] Decay property of solutions for damped wave equations with space-time dependent damping term (2011)
  • Author(s): J.Lin, K. Nishihara, J.Zhai
  • Journal Title: J.Math.Anal.Appl. 374 Pages: 602-614
  • Peer Reviewed
• [Journal Article] $L^2$ estimates of solutions for damped wave equations with space-time dependent damping term (2010)
  • Author(s): J.Lin, K. Nishihara, J.Zhai
  • Journal Title: J.Differential Equations 248 Pages: 403-422
  • Peer Reviewed
• [Journal Article] Decay properties for the damped wave equation with space dependent potential and absorbed semilinear term (2010)
  • Author(s): K. Nishihara
  • Journal Title: Commun. Partial Differential Equations 35 Pages: 1402-1418
  • Peer Reviewed
• [Journal Article] 消散型波動方程式のコーシー問題の解の拡散現象 (2010)
  • Author(s): 西原健二
  • Journal Title: 数学 62巻 Pages: 164-181
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of solutions for the damped wave equation with slowly decaying data (2008)
  • Author(s): T.Narazaki, K. Nishihara
  • Journal Title: J.Math.Anal.Appl. 338 Pages: 803-819
  • Peer Reviewed
• [Presentation] Large time behavior of solutions to the Cauchy problem for the damped wave equation with absorbing semilinear term (2010)
  • Author(s): 西原健二
  • Organizer: Kinetic Equations and Hyperbolic Conservation Laws
  • Place of Presentation: National University of Singapore, Singapore
  • Year and Date: 2010-11-30
• [Presentation] Asymptotic behavior of solutions to the Cauchy problem for the weakly coupled damped wave system (2010)
  • Author(s): 西原健二
  • Organizer: International Workshop on Partial Differential Equations and Mathematical Physics
  • Place of Presentation: Zhejiang University of Technology, Hangzhou, China
  • Year and Date: 2010-10-31
• [Presentation] Large time behavior of solutions to the Cauchy problem for the semilinear damped wave equation (2010)
  • Author(s): 西原健二
  • Organizer: 2010 Chinese-German conference on fluid and gas dynamics
  • Place of Presentation: Zhejiang Normal University, Jinhua, China
  • Year and Date: 2010-05-22
• [Presentation] Behavior of solutions for the semilinear heat equation and damped wave equation with slowly decaying data (2008)
  • Author(s): 西原健二
  • Organizer: AIMS Seventh International Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: University of Texas at Arlington, USA
  • Year and Date: 2008-05-19