Exponential Stability for Damped Shear Beam Model and New Facts Related to the Classical Timoshenko System With a Distributed Delay Term

Abstract

We consider in this manuscript  a Timoshenko type beam model with a distributed delay term.  If the distributed delay term is small enough, we prove the global existence of solutions by using the Faedo-Galerkin approximations together with some energy estimates. Under suitable assumptions, we prove exponential stability of the solution. This result is obtained by introducing a suitable Lyapounov function.