Optimal regularity and optimal control of a thermoelastic structural acoustic model with point control and clamped boundary conditions

In this paper we consider point control of a structural acoustic model with thermoelastic effects. The key feature of this paper is that the two-dimensional plate modeling the active wall of the acoustic chamber has clamped boundary conditions. For this case a new optimal regularity result has recently become available (Triggiani, 2008). Using this new result for the plate alone, we derive a sharp (optimal) regularity result for the overall coupled system of wave and thermoelastic plate equations, after overcoming a series of additional technical difficulties. This allows for the study of an optimal control problem of the coupled system.