PDE Seminar (2018/5/25): Sharp asymptotics for the generalized KdVB equation with slowly decaying data

2018-5-25 16:30 - 2018-5-25 17:30
Faculty of Science Building #3, Room 309
Ikki Fukuda (Hokkaido University)
We consider the asymptotic behavior of the global solution to the initial value problem for the generalized Korteweg-de Vries-Burgers (KdVB) equation with slowly decaying data. The solution to this problem converges to a self-similar solution to the Burgers equation called a nonlinear diffusion wave. In this talk, we focus on the decay rate of the initial data, and we will investigate the optimal asymptotic rate to the nonlinear diffusion wave which corresponds to the decay rate of the initial value, by constructing the second asymptotic profile.