EVENT DETAILS AND ABSTRACT

Title: Revisit the damped wave equation on $T^2$
Speaker: Chenmin Sun
Speaker Info: Cergy-Pontoise
Brief Description:
Special Note:
Abstract:

We consider the damped wave equation on the two-dimensional torus where the damped region does not satisfy the geometric control condition. It turns out that the energy decay rate depends both on the vanishing behavior of the damping and the shape of the interface between the damped and the undamped region. In particular, with the same vanishing order, the convex-shaped damping can better stabilizes the wave than the rectangular-shaped damping. The main ingredient in the proof is the averaging method (normal form) developed in the work of Sj\"ostrand and Hitrik. As a by-product, we can recover a theorem of Anantharaman-Léautaud ( Anal.&PDE 2014) with a different proof.