Boundary stabilization of a 3-dimensional structural acoustic model

The main result of this paper provides uniform decay rates obtained for the energy function associated with a three-dimensional structural acoustic mo del described by coupled system consisting of the wave equation and plate e quation with the coupling on the interface between the acoustic chamber and the wall. The uniform stabilization is achieved by introducing a nonlinear dissipation acting via boundary forces applied at the edge of the plate an d viscous or boundary damping applied to the wave equation. The results obt ained in this paper extend, to the non-analytic, hyperbolic-like setting, t he results obtained previously in the literature for acoustic problems mode led by structurally damped plates (governed by analytic semigroups). As a bypass product, we also obtain optimal uniform decay rates for the Eul er Bernoulli plate equations with nonlinear boundary dissipation acting via shear forces only and without (i) any geometric conditions imposed on the domain,(ii) any growth conditions at the origin imposed on the nonlinear fu nction. This is in contrast with the results obtained previously in the lit erature ([22] and references therein). (C) Elsevier, Paris.