Boundary stabilizability of nonlinear structural acoustic models with thermal effects on the interface

A three-dimensional structural acoustic model is considered. This model con sists of a wave equation defined on a 3-dimensional bounded domain Omega co upled with a thermoelastic plate equation defined on Gamma(0) - a flat surf ace of the boundary partial derivative Omega. The main issue studied hers i s that of uniform stabilizability of the overall interactive model. Since t he original (uncontrolled) model is only strongly stable, but not uniformly stable, the question becomes: what is the 'minimal amount' of dissipation necessary to obtain uniform decay rates for the energy of the overall syste m? Our main result states that boundary nonlinear dissipation placed only o n a suitable portion of the part of the boundary which is complementary to Gamma(0), suffices for the stabilization of the entire structure. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.