Optimal control of a structural acoustic model with flexible curved walls

The aim of this paper is to investigate the controllability properties of a coupled system of partial differential equations which arises in structural acoustic applications. We consider an acoustic chamber with a structurally damped, flexible curved wall, subjected to a feedback control effected by means of piezoceramic patch actuators. The shell model used here is based on intrinsic geometric methods, and was derived and shown to be uniformly stable in a joint paper of the authors with Irena Lasiecka and Jean-Paul Zolesio [5]. Here we show the companion result of synthesis of the optimal control by first modeling the piezoceramic patches in terms of the intrinsic geometry, and then deriving the necessary singularity estimate for the system.