In this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of solutions using the semi-group theory. Moreover, we establish an explicit and general decay result for a wide class of relaxation functions, which depend on a stability number μ.

In this work, we consider the Lamé system in 3-dimension bounded domain with infinite memories. We prove, under some appropriate assumptions, that this system is well-posed and stable, and we get a general and precise estimate on the convergence of solutions to zero at infinity in terms of the growth of the infinite memories.

In this paper we consider second order evolution equations with bounded damping. We give a characterization of a non-uniform decay for the damped problem using a kind of observability estimate for the associated undamped problem.