A STABILITY RESULT FOR A TIMOSHENKO SYSTEM WITH PAST HISTORY AND A DELAY TERM IN THE INTERNAL FEEDBACK

In this paper we consider a Timoshenko system with a delay term in the feedback and memory term. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove a well posedness result. Furthermore an exponential stability result has been shown if the weight of the damping is greater or equal to the weight of the delay. We distinguish two cases: the case where the weight of the delay is less than the weight of the damping and the case where the two weights are equal. In each case we introduce an appropriate Lyapunov functional which leads to an exponential stability. This result extends the one in [15] and the recent result in [23].