Regularity and asymptotic behaviour for a damped plate-membrane transmission problem
Analysis of PDEs
2020-08-20 v1
Abstract
We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponential stability holds in the damped-damped situation and polynomial stability (but no exponential stability) holds in the damped-undamped case. Additionally, we show that the solutions first defined by the weak formulation, in fact have higher Sobolev space regularity.
Cite
@article{arxiv.1807.09730,
title = {Regularity and asymptotic behaviour for a damped plate-membrane transmission problem},
author = {Bienvenido Barraza Martinez and Robert Denk and Jairo Hernandez Monzon and Felix Kammerlander and Max Nendel},
journal= {arXiv preprint arXiv:1807.09730},
year = {2020}
}