Acoustic wave motions stabilized by boundary memory damping

We consider the linear wave equation with acoustic boundary conditions (ABC) on a portion Γ1Γ1 of the boundary and Dirichlet conditions on the rest of the boundary. The ABC contain a damping term of memory type with respect to the normal displacement of the point of Γ1Γ1. Under some assumption on the memory kernel, we show that the associated operator matrix generates a strongly continuous semigroup of contractions on a Hilbert space, and the semigroup is strongly stable.