General decay for a viscoelastic damped Timoshenko system of second sound with distributed delay

Abstract

In this paper we consider a thermo-viscoelastic system of Timoshenko-type with nonlinear damping and a distributed delay acting on transverse displacement. The heat flux of the system is governed by Cattaneo's law. We use the energy method and some properties of convex functions to prove, regardless of the speeds of wave propagation, general decay estimate from which the exponential, logarithmic and polynomial types of decay are only special cases.