Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation
Optimization and Control
2012-12-03 v1 Analysis of PDEs
Abstract
We study a damped semi-linear wave equation in a bounded domain with smooth boundary. It is proved that any sufficiently smooth solution can be stabilised locally by a finite-dimensional feedback control supported by a given open subset satisfying a geometric condition. The proof is based on an investigation of the linearised equation, for which we construct a stabilising control satisfying the required properties. We next prove that the same control stabilises locally the non-linear problem.
Cite
@article{arxiv.1211.7202,
title = {Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation},
author = {Kaïs Ammari and Thomas Duyckaerts and Armen Shirikyan},
journal= {arXiv preprint arXiv:1211.7202},
year = {2012}
}
Comments
29 pages