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arXiv · 1211.7202

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

Kaïs Ammari·Thomas Duyckaerts·Armen Shirikyan
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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.

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Kaïs Ammari, Thomas Duyckaerts, Armen Shirikyan. 2012-11-30. Local feedback stabilisation to a non-stationary solution for a damped non-linear wave equation. https://arxiv.org/abs/1211.7202

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