Exact controllability of structural acoustic interactions


In this article, we work to discern exact controllability properties of two coupled wave equations, one of which holds on the interior of a bounded open domain Ω, and the other on a segment Γ0 of the boundary ∂Ω. Moreover, the coupling is accomplished through terms on the boundary. Because of the particular physical application involved-the attenuation of acoustic waves within a chamber by means of active controllers on the chamber walls-control is to be implemented on the boundary only. We give here concise results of exact controllability for this system of interactions, with the control functions being applied through ∂Ω. In particular, it is seen that for special geometries, control may be exerted on the boundary segment Γ0 only. Moreover, this reachability problem is posed and solved on the finite energy spaces which are "natural" to the respective wave components; namely, H1×L2. In this work, we make use of microlocal estimates derived for the Neumann-control of wave equations, as well as a special vector field which is now known to exist under certain geometrical situations. © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.

Publication Title

Journal des Mathematiques Pures et Appliquees