UNIFORM DECAY IN WEAKLY DISSIPATIVE TIMOSHENKO SYSTEM WITH INTERNAL DISTRIBUTED DELAY FEEDBACKS

In this paper we consider one-dimensional Timoshenko system with linear frictional damping and a distributed delay acting on the displacement equation. Under suitable assumptions on the weight of the delay and the wave speeds, we establish the well-posedness of the system and show that the dissipation through the frictional damping is strong enough to uniformly stabilize the system even in the presence of delay.