Exponential Decay and Numerical Solution for a Timoshenko System with Delay Term in the Internal Feedback

In this work we study the asymptotic behavior as t → ∞ of the solution for the Timoshenko system with delay term in the feedback. We use the semigroup theory for to prove the well-posedness of the system and for to establish the exponential stability. As far we know, there exist few results for problems with delay, where the asymptotic behavior is based on the Gearhart- Herbst-Pruss-Huang theorem to dissipative system. See [4], [5], [6]. Finally, we present numerical results of the solution of the system.