Boundary stabilization of structural acoustic interactions with interface on a Reissner–Mindlin plate

Boundary stabilization of a structural acoustic model comprised of a wave and a Reissner–Mindlin plate is addressed. Both the components of the dynamics are subject to localized nonlinear boundary damping: the acoustic dissipative feedback is restricted to the flexible boundary and only a portion of the rigid wall; the plate is damped only on a segment of its edge.Derivation of stabilization/observability inequalities for a coupled system requires weighted energy multipliers dependent on the geometry of the domain, and special microlocal trace estimates for the Reissner–Mindlin plate. The behavior of the energy at infinity can be quantified by a solution to an explicitly constructed nonlinear ODE. The nonlinearities in the feedbacks may include sub- and superlinear growth at infinity, in which case the decay scheme presents a trade-off between the regularity of trajectories and attainable uniform dissipation rates of the finite energy.