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In this paper, we investigate a Bresse-Timoshenko-type system with a distributed delay term and second sound. Under suitable assumptions, we establish the global well-posedness of the initial and boundary value problem by using the Faedo-Galerkin approximations and some energy estimates.

In this work, we consider a one-dimensional Timoshenko system of thermoelasticity of type III with past history and distributive delay. It is known that an arbitrarily small delay may be the source of instability. We establish the stability of the system for the cases of equal and nonequal speeds of wave propagation respectively. 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 and improve the related results.