Local decay and asymptotic profile for the damped wave equation in the asymptotically Euclidean setting
De Rayan Fahs
Apparaît dans la collection : Wave propagation in guiding structures / Propagation d'ondes dans les structures guidées
We consider the question of energy decay for the (possibly damped) wave equation in the asymptotically Euclidean setting. In even dimensions, we go beyond the optimal decay by providing the large time asymptotic profile, given by a solution of the free wave equation. In odd dimensions, we improve the best known estimates, and in particular, we go beyond the decay rate which is optimal in even dimensions. The analysis mainly relies on a comparison of the corresponding resolvent with the resolvent of the free problem for low frequencies. Moreover, all the results hold for the damped wave equation with a short-range absorption index.This is a joint work with Julien Royer.
