On the study of evolution equations from hyperbolic ones

2009 Fiscal Year Self-evaluation Report

• Project/Area Number: 19340030
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka University
• Principal Investigator: HAYASHI Nakao Osaka University, 大学院・理学研究科, 教授 (30173016)
• Project Period (FY): 2007 – 2010
• Keywords: 非線形Klein-Gordon方程式 / 非線形Schredinger方程式 / 双曲型方程式 / 分散型方程式

Research Abstract

(1)分散型方程式固有の作用素の研究
(2)臨界冪を非線形項に持つ方程式の研究に不可欠な位相関数の研究
(3)新しい関数空間、解の平滑化、位相関数の非線形分散型方程式への応用
(4)Korteweg-de Vries型方程式、3次の非線形項をもつ1次元非線形型Klein-Gordon方程式の解の漸近的振る舞いを明確にする。

Research Products

• [Journal Article] Final state problem for the cubic nonlinear Klein-Gordon equation (2009)
  • Author(s): N. Hayashi, P. I. Naumkin
  • Journal Title: J. Math. Phys. vol. 50, no. 10 Pages: 103511-14
  • Peer Reviewed
• [Journal Article] Asymptotic properties of solutions to dispersive equation of Schredinger type (2008)
  • Author(s): N. Hayashi, P. I. Naumkin
  • Journal Title: J. Math. Soc. Japan vol. 60 Pages: 631-652
  • Peer Reviewed
• [Journal Article] The initial value problem and asymptotics of solutions for the cubic nonlinear Klein-Gordon equation (2008)
  • Author(s): N. Hayashi, P. I. Naumkin
  • Journal Title: Zeitschrift fur Angewandte Mathematik und Physik vol. 59, no. 6 Pages: 1002-1028
  • Peer Reviewed
• [Presentation] 非線形 Klein-Gordon 方程式の散乱問題 (2009)
  • Author(s): 林仲夫
  • Organizer: 日本数学会, 解析学賞受賞特別講演
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-26