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

20151116 16:30 
20151116 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 selfsimilar 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).