Uniform Decaying Property of Solutions for Anisotropic Viscoelastic Systems

Abstract

The paper concerns about the uniform decaying property (abbreviated by UDP) of solutions for an anisotropic viscoelastic system in the form of integrodifferential system (abbreviated by VID system) with mixed type boundary condition. The mixed type condition consists of the homogeneous displacement boundary condition and a homogeneous traction boundary condition or with a dissipation. By using a dissipative structure of this system, we will prove the UDP in a unified way for the two cases, which are, when the time derivative of relaxation tensor decays with polynomial order and it decays with exponential order.