Control-theoretic properties of structural acoustic models with thermal effects, II. Trace regularity results

Abstract: We consider a structural acoustic model with the flexible wall modeled by a thermoelastic plate, subject to Dirichlet boundary control in the thermal component. We establish sharp reularity for the traces of the thermal variable on the boundary in case the system is supplemented with clamped mechanical boundary conditions. These trace estimates are most crucial for validity of the optimal control theoiry developed by 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.