Luci Harue Fatori

The optimal decay rate for a weak dissipative Bresse system

Abstract In this work we consider the Bresse system with frictional damping operating only on the angle displacement and we show that under a certain assertion the solution decays polynomially and the decay rate is optimal.

TRANSMISSION PROBLEM FOR HYPERBOLIC THERMOELASTIC SYSTEMS

In this article we study a transmission problem in thermoelasticity. We show that the linear system is well posed and that the solution decays exponentially to zero as time goes to infinity. That is, denoting by E(t) the first-order energy associated to the thermoelastic system, there exists positive constants c and n such that E(t) h cE (0) e m n t .

Regularizing Properties and Propagations of Singularities for Thermoelastic Plates

We consider the thermoelastic plate system, u u - γΔ tt + Δ 2 u + αΔθ = 0, θ t - κΔθ - αΔu t = 0 and we make a comparison between the models in which γ = 0 and γ > 0. We conclude that in the first case the plate system is of a parabolic type, while when γ > 0 the corresponding system has a hyperbolic behaviour.

Energy decay to Timoshenko's system with thermoelasticity of type III

We consider the thermoelastic beam system when the oscillations are defined by the Timoshenkos model and the heat conduction is given by Green and Naghdi theories. Our main result is that the corresponding semigroup is exponentially stable if and only if the wave speeds associated to the hyperbolic part of the system are equal. In the case of lack of exponential stability we show that the solution decays polynomially and we prove that the rate of decay is optimal.

The Timoshenko system with history and Cattaneo law

In this paper we study a fully hyperbolic thermoelastic Timoshenko system with past history where the thermal effects are given by Cattaneos law. We obtain exponential stability of solutions if and only if a new condition on the wave speed of propagation is verified. Otherwise, when that condition fails, we obtain polynomial stability of solutions. In this case optimal rates of decay are established.

A thermoelastic system of memory type in noncylindrical domains

In this paper, we consider a hyperbolic thermoelastic system of memory type in domains with moving boundary. The problem models vibrations of an elastic bar under thermal effects according to the heat conduction law of Gurtin and Pipkin. Global existence is proved by using the penalty method of Lions.

Stability conditions to Bresse systems with indefinite memory dissipation

ABSTRACT We study the asymptotic behavior of Bresse system with non-dissipative kernel memory acting only in the equation of longitudinal displacement. We show that the exponential stability depends on conditions regarding the decay rate of the kernel and a new relationship between the coefficients of the system. Moreover, this new condition on the constants of the system is used to prove strong stability and exponential stability for the homogeneous case (frictional dissipation in the longitudinal equation).