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

Francesca Bucci. "Control-theoretic properties of structural acoustic models with thermal effects, II. Trace regularity results." Applicationes Mathematicae 35.3 (2008): 305-321. <http://eudml.org/doc/280053>.

@article{FrancescaBucci2008,
abstract = {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.},
author = {Francesca Bucci},
journal = {Applicationes Mathematicae},
keywords = {structural acoustic model; thermoelastic plates; boundary control; Riccati equations; trace regularity},
language = {eng},
number = {3},
pages = {305-321},
title = {Control-theoretic properties of structural acoustic models with thermal effects, II. Trace regularity results},
url = {http://eudml.org/doc/280053},
volume = {35},
year = {2008},
}

TY - JOUR
AU - Francesca Bucci
TI - Control-theoretic properties of structural acoustic models with thermal effects, II. Trace regularity results
JO - Applicationes Mathematicae
PY - 2008
VL - 35
IS - 3
SP - 305
EP - 321
AB - 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.
LA - eng
KW - structural acoustic model; thermoelastic plates; boundary control; Riccati equations; trace regularity
UR - http://eudml.org/doc/280053
ER -