PDE Seminar (2015/11/16): Asymptotic behavior of solutions for the damped wave equation with a nonlinear convection term

Date
2015-11-16 16:30 - 2015-11-16 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Masakazu Kato (Muroran Institute of Technology)
 
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).