Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping
Optimization and Control
2020-11-17 v3 Analysis of PDEs
Abstract
In this paper, we study input-to-state (ISS) issues for damped wave equations with Dirichlet boundary conditions on a bounded domain of dimension two. The damping term is assumed to be non-linear and localized to an open subset of the domain. In a first step, we handle the undisturbed case as an extension of a previous work, where stability results are given with a damping term active on the full domain. Then, we address the case with disturbances and provide input-to-state types of results.
Keywords
Cite
@article{arxiv.2005.06206,
title = {Weak Input to state estimates for 2D damped wave equations with localized and non-linear damping},
author = {Meryem Kafnemer and Benmiloud Mebkhout and Yacine Chitour},
journal= {arXiv preprint arXiv:2005.06206},
year = {2020}
}