General stability for a Timoshenko-type system with a nonlinear damping term

Abstract

In this paper, we consider a one-dimensional Timoshenko system with a nonlinear damping term. First, we show the existence and uniqueness of the solution by using the semi-group method, more precisely by the Hille-Yosida theorem. Also, by constructing a suitable Lyapunov functional and using some properties of convex functions, we establish a general decay result for the solution of the system. Moreover, our result does not depend on any relation between the parameters of the system.