A coupled model of piezoelectric beams with magnetic effect and nonlinear damping is considered. Assuming adequate hypotheses on nonlinear damping, uniform decay rates for the solution is established.

In this paper, we investigate the decay properties of the thermoelastic Bresse system in the whole space. We consider many cases depending on the parameters of the model and we establish new decay rates. We need to mention here that, in some cases we don't have the regularity-loss phenomena as in the previous works in the literature. To prove our results, we use the energy method in the Fourier space to build a very delicate Lyapunov functionals that give the desired results.

In this paper, we investigate the decay properties of suspension bridge with memories in one dimension. To prove our results, we use the energy method to build some very delicate Lyapunov functionals that give the desired results.

In this paper, we investigate the decay properties of the thermoelastic Timoshenko system with past history in the whole space where the thermal effects are given by Cattaneo and Fourier laws. We obtain that both systems, Timoshenko-Fourier and Timoshenko-Cattaneo, have the same rate of decay (1+t)^{-(1/4)} and the regularity-loss type property is not present in some cases. Moreover, new stability number χ is introduced, such new number controls the decay rate of the solution with respect to the regularity of the initial data. To prove our results, we use the energy method in Fourier space to build an appropriate Lyapunov functionals that give the desired results.