Exponential stability for the Timoshenko system with two weak dampings

In this paper we consider a linear system of Timoshenko type beam equations with frictional dissipative terms. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng and their collaborators in past years. This method is very different from some others in the literature, such as the traditional energy method. It is our hope that the reader will find the method presented in this work is powerful and simple.