Local energy decay and smoothing effect for the damped Schr{\"o}dinger equation
Mathematical Physics
2018-03-16 v1 Analysis of PDEs
math.MP
Abstract
We prove the local energy decay and the smoothing effect for the damped Schr{\"o}dinger equation on R^d. The self-adjoint part is a Laplacian associated to a long-range perturbation of the flat metric. The proofs are based on uniform resolvent estimates obtained by the dissipative Mourre method. All the results depend on the strength of the dissipation which we consider.
Keywords
Cite
@article{arxiv.1505.07200,
title = {Local energy decay and smoothing effect for the damped Schr{\"o}dinger equation},
author = {Moez Khenissi and Julien Royer},
journal= {arXiv preprint arXiv:1505.07200},
year = {2018}
}