Exponential stability for a thermo-viscoelastic Timoshenko system with fading memory

Abstract

We are concerned with the characterization of the (uniform) exponential stability for a thermo-viscoelastic Timoshenko beam system under the Fourier law for heat conduction and memory in a history setting. Motivated by [5,6], we explore an intrinsic (non differentiable) assumption on the memory kernel that provides a necessary and sufficient condition for the exponential stability of the whole system. It gives a substantial generalization of the stability results obtained in [10,14,18] and surely ties up loose ends about the hypothesis equivalent to exponential stability of the problem.