Higidio Portillo Oquendo

Optimal decay for coupled waves with Kelvin–Voigt damping

We consider a system of two coupled waves where one is conservative and the other is dissipative. When the dissipation is caused by an internal friction, Alabau et al. (2002), showed the polynomial decay of the associated semigroup with decay rate t−1∕2. In this paper, we substitute the friction damping by another one. This damping is of Kelvin–Voigt type, and for this system, we show that the semigroup loses speed and decays with the rate t−1∕4. Moreover, we prove that this decay rate is optimal.

A transmission problem for beams on nonlinear supports

A transmission problem involving two Euler-Bernoulli equations modeling the vibrations of a composite beam is studied. Assuming that the beam is clamped at one extremity, and resting on an elastic bearing at the other extremity, the existence of a unique global solution and decay rates of the energy are obtained by adding just one damping device at the end containing the bearing mechanism.

Uniform decay for a plate equation partially dissipative

In this article we consider a plate made of by two types of materials: a part is conservative and the other dissipative. We show that the dissipation produced for the second part is strong enough to obtain the uniform decay of the energy. Moreover, we found that the rate of decay of the solutions depend on behavior of the dissipative term in a neighborhood of zero, that is, for a linear dissipation we obtain exponential decay while for a polynomial dissipation we obtain polynomial decay.