Global existence and energy decay of solutions to a viscoelastic Timoshenko beam system with a nonlinear delay term

Abstract

In this paper, we consider the viscoelastic Timoshenko beam system with a delay term in the weakly nonlinear internal feedback in a bounded domain:We prove a global existence result using the energy method combined with the Faedo- Galerkin procedure under a condition between the weight of delay term in the feedback and the weight of the term without delay. Furthermore, we study the asymptotic behavior of solutions using a perturbed energy method.