Existence and stability results of a nonlinear Timoshenko equation with damping and source terms

Abstract

In this paper, we consider a nonlinear Timoshenko equation. First, we prove the local existence solution by the Faedo?Galerkin method, and, under suitable assumptions with positive initial energy, we prove that the local existence is global in time. Finally, the stability result is established based on Komornik?s integral inequality.