偏微分方程式セミナー(2015/11/16): Asymptotic behavior of solutions for the damped wave equation with a nonlinear convection term, 加藤 正和 氏

開催日時
2015年   11月 16日 16時 30分 ~ 2015年   11月 16日 17時 30分
場所
北海道大学理学部3号館3-309室
講演者
加藤 正和 氏 (室蘭工業大学)
 
In this talk, we consider large time behavior of solutions to the initial value problem for the damped wave equation with a nonlinear convection term. It is well known that the global solutions tend to the nonlinear diffusion waves which are self-similar solutions of the Burgers equation. We obtain the optimal convergence rate of the solutions to the nonlinear waves by studying the second asymptotic profile. The similar estimate was obtained for the generalized Burgers equation. By comparing the difference of the asymptotic profile between the damped wave equation and the Burges equation, we make it clear that the optimal decay rate heavily depends on the structure of the nonlinearity. This talk is based on a joint work with Prof. Yoshihiro Ueda (Kobe University).

関連項目

研究集会・セミナー・集中講義の一覧へ