Asymptotic Behavior of a Vibrating Membrane Model

Abstract

We study the asymptotic behaviour of the solutions of an approximated model of the vibrating membrane. The results we give concern three different approximations; for each the boundedness of the energy and the presence of an absorbing set are proved, provided that the forcing term remains bounded in a suitable norm. The absorbing set is found via a known technique, while the boundedness of the energy is obtained by "ad hoc" calculations. Moreover, in one approximation, in the autonomous case, the existence of an attractor is proved.