Control-theoretic Properties of Structural Acoustic Models with Thermal Effects, Ii. Trace Regularity Results

We consider a structural acoustic problem with the flexible wall modeled by a thermoelastic plate, subject to Dirichlet boundary control in the thermal component. We establish sharp regularity results for the traces of the thermal variable on the boundary, in the case the system is supplemented with clamped mechanical boundary conditions. These regularity estimates are most crucial for validity of the optimal control theory developed in [Acquistapace et al., Adv. Differential Equations, 2005], which ensures well-posedness of the corresponding differential Riccati equations. The proof takes full advantage of the exceptional boundary regularity of the mechanical component of the clamped thermoelastic system as well as of the sharp trace theory pertaining to wave equations with Neumann boundary data.