English

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.

Keywords

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}
}