Existence and Asymptotic Stability of the Solution for the Timoshenko Transmission System with Distributed Delay

Abstract

In the present paper, a transmission problem of the Timoshenko beam in the presence of distributed delay is considered. Under appropriate assumptions, we prove the well-posedness by using the semi-group theory. Furthermore, we study the asymptotic behavior of solutions using the multiplier method. We investigate the techniques and ideas used by the second author to extend the recent results.