Energy decay for a system of Schr{\"o}dinger equations in a wave guide
Analysis of PDEs
2021-11-11 v1 Mathematical Physics
math.MP
Abstract
We prove exponential decay for a system of two Schr{\"o}dinger equations in a wave guide, with coupling and damping at the boundary. This relies on the spectral analysis of the corresponding coupled Schr{\"o}dinger operator on the one-dimensional cross section. We show in particular that we have a spectral gap and that the corresponding generalized eigenfunctions form a Riesz basis.
Cite
@article{arxiv.2111.05580,
title = {Energy decay for a system of Schr{\"o}dinger equations in a wave guide},
author = {Radhia Ayechi and Ilhem Boukhris and Julien Royer},
journal= {arXiv preprint arXiv:2111.05580},
year = {2021}
}