Uniform and weak stability of Bresse system with one infinite memory in the shear angle displacements

In this paper, we consider a one-dimensional linear Bresse system in a bounded open interval with one infinite memory acting only on the shear angle equation. First, we establish the well posedness using the semigroup theory. Then, we prove two general (uniform and weak) decay estimates depending on the speeds of wave propagations and the arbitrary growth at infinity of the relaxation function.

Uniform decay rates of a Bresse thermoelastic system in the whole space

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.

A new stability result for a thermoelastic Bresse system with viscoelastic damping

We investigate a thermoelastic Bresse system with viscoelastic damping acting on the shear force and heat conduction acting on the bending moment. We show that with weaker conditions on the relaxation function and physical parameters, the solution energy has general and optimal decay rates. Some examples are given to illustrate the findings.

A New Result of Stability for Thermoelastic-Bresse System of Second Sound Related with Forcing, Delay, and Past History Terms

We consider a one-dimensional linear thermoelastic Bresse system with delay term, forcing, and infinity history acting on the shear angle displacement. Under an appropriate assumption between the weight of the delay and the weight of the damping, we prove the well-posedness of the problem using the semigroup method, where an asymptotic stability result of global solution is obtained.

General decay of solutions of a thermoelastic Bresse system with viscoelastic boundary conditions

In this paper we consider a multidimensional thermoviscoelastic system of Bresse type where the heat conduction is given by Green and Naghdi theories. For a wider class of relaxation functions, We show that the dissipation produced by the memory eect is strong enough to produce a general decay results. We establish a general decay results, from which the usual exponential and polynomial decay rates are only special cases.

New stability result for a Bresse system with one infinite memory in the shear angle equation

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory acting in the second equation (the shear angle equation) of the system. We prove that the asymptotic stability of the system holds under some general condition imposed into the relaxation function, precisely,</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ g^{\prime}(t)\le -\xi(t) G(g(t)). $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>The proof is based on the multiplier method and makes use of convex functions and some inequalities. More specifically, we remove the constraint imposed on the boundedness condition on the initial data <inline-formula><tex-math id="M1">\begin{document}$ \eta{0x} $\end{document}</tex-math></inline-formula>. This study generalizes and improves previous literature outcomes.</p>