Local feedback stabilisation for a damped semi-linear wave equation

Nom de l'orateur
Kais Ammari
Etablissement de l'orateur
Monastir
Date et heure de l'exposé
Lieu de l'exposé
Salle des séminaires

We study a damped semi-linear wave equation in a bounded domain of R^3 with smooth boundary. It is proved that any H^2-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. This is a joint work with Thomas Duyckaerts and Armen Shirikyan.