Global existence and stability results for a nonlinear Timoshenko system of thermoelasticity of type III with delay

In this paper, we consider a nonlinear thermoelastic system of Timoshenko type with delay. It is known that an arbitrarily small delay may be the source of instability. The delay term works on the second equation which describes the motion of a rotation angle. We establish the well-posedness and the stability of the system for the cases of equal and nonequal speeds of wave propagation. Our results show that the damping effect is strong enough to uniformly stabilize the system even in the presence of time delay under suitable conditions by using perturbed energy functional technique and improve the related results.