Stabilization of Viscoelastic Wave Equations with Distributed or Boundary Delay

Abstract

The wave equation with viscoelastic boundary damping and internal or boundary delay is considered. The memory kernel is assumed to be integrable and completely monotonic. Under certain conditions on the damping factor, delay factor and the memory kernel it is shown that the energy of the solutions decay to zero either asymptotically or exponentially. In the case of internal delay, the result is obtained through spectral analysis and the Gearhart-Pruss Theorem, whereas in the case of boundary delay, it is obtained using the energy method.