Well-posedness and exponential stability for a linear damped Timoshenko system with second sound and internal distributed delay

Abstract

In this article we consider one-dimensional linear thermoelastic system of Timoshenko type with linear frictional damping and a distributed delay acting on the displacement equation. The heat flux of the system is governed by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we establish the well-posedness result and prove that the system is exponentially stable regardless of the speeds of wave propagation.

Keywords

• Timoshenko system
• second sound well-posedness
• exponential stability
• distributed delay