Lack of exponential decay in viscoelastic materials with voids

Abstract

We study the stability of solutions to a coupled evolution system associated with an isotropic porous and centrosymmetric viscoelastic solid with porous dissipation (a porous elastic system with history). With the help of the method of the semigroup theory and some novel observations, we prove successfully that the condition of equal wave-speed propagation is still necessary for exponential stability of the system in the case of Dirichlet–Dirichlet boundary conditions.