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.
Cite this article
M. Boella, Asymptotic Behavior of a Vibrating Membrane Model. Z. Anal. Anwend. 23 (2004), no. 1, pp. 39–66DOI 10.4171/ZAA/1187