Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation

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 inve...

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Bibliographic Details
Main Authors Ammari, Kaïs, Duyckaerts, Thomas, Shirikyan, Armen
Format Journal Article
LanguageEnglish
Published 30.11.2012
Subjects
Mathematics - Analysis of PDEs
Mathematics - Optimization and Control
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Summary: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.
DOI:10.48550/arxiv.1211.7202