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

Francesca Bucci¹

¹ Dipartimento di Matematica Applicata Università degli Studi di Firenze Via S. Marta 3, I-50139 Firenze, Italy

Applicationes Mathematicae, Tome 35 (2008) no. 3, pp. 305-321

Résumé

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 case the system is supplemented with clamped mechanical boundary conditions. These regularity estimates are most crucial for validity of the optimal control theory 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.

Détail

DOI : 10.4064/am35-3-4

Keywords: consider structural acoustic problem flexible wall modeled thermoelastic plate subject dirichlet boundary control thermal component establish sharp regularity results traces thermal variable boundary system supplemented clamped mechanical boundary conditions these regularity estimates crucial validity optimal control theory developed acquistapace adv differential equations which ensures well posedness corresponding differential riccati equations proof takes full advantage exceptional boundary regularity mechanical component clamped thermoelastic system sharp trace theory pertaining wave equations neumann boundary