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.

Keywords

• Timoshenko system
• transmission problem
• distributed delay
• asymptotic behavior
• multiplier method