Exact controllability of structural acoustic interactions

Abstract

In this paper, we work to discern exact controllability properties of two coupled wave equations, one of which holds on the interior of a bounded open domain , and the other on a segment 0 of the boundary \partial . 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 \partial . In particular, it is seen that for special geometries, control may be exerted on the boundary segment 0 only. We make use here 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.