Hugo D. Fernández Sare

On the stability of Mindlin-Timoshenko plates

We consider a Mindlin-Timoshenko model with frictional dissipations acting on the equations for the rotation angles. We prove that this system is not exponentially stable independent of any relations between the constants of the system, which is different from the analogous one-dimensional case. Moreover, we show that the solution decays polynomially to zero, with rates that can be improved depending on the regularity of the initial data.

Stability for a Transmission Problem in Thermoelasticity with Second Sound

We consider a semilinear transmission problem for a coupling of an elastic and a thermoelastic material. The heat conduction is modeled by Cattaneos law removing the physical paradox of infinite propagation speed of signals. The damped, totally hyperbolic system is shown to be exponentially stable, and the existence of a global attractor is shown.

Optimal rates of decay in 2-d thermoelasticity with second sound

We consider a linear thermoelastic plate system where the heat flux is given by Cattaneos model. We show that the resulting system is exponentially stable if and only if the rotational inertia coefficient μ is positive. On the other hand, for μ = 0, we establish polynomial stability results giving optimal rates of decay for initial data in the domain of the infinitesimal generator of the thermoelastic semigroup.

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.

Analyticity of transmission problem to thermoelastic plates

In this paper we consider an oscillation model to a plate comprised of two different thermoelastic materials; that is, we study a transmission problem to thermoelastic plates. Our main result is to prove that the corresponding semigroup associated to this problem is of analytic type.