Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

In this talk, we will show a null-controllability result of a fluid-structure interaction system characterized by the heat equation and by an elastic structure governed by a damped beam equation. The beam is located on a part of the boundary. The controls act on arbitrary small subsets of the heat domain and of the beam domain. In order to show that the system is null-controllable, we show an observability inequality for the adjoint system. We first show a Carleman estimate for the heat equation and for the damped beam equation separately. Secondly, we combine the two Carleman estimates to get a final Carleman estimate for the adjoint system. Then, finally the observability inequality is obtain thanks to the Carleman estimate.

This is a joint work with M. Badra and J. Dardé.