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Zeitschrift für Analysis und ihre Anwendungen


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Volume 23, Issue 1, 2004, pp. 39–66
DOI: 10.4171/ZAA/1187

Published online: 2004-03-31

Asymptotic Behavior of a Vibrating Membrane Model

M. Boella[1]

(1) Politecnico, Milano, Italy

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.

Keywords: Absorbing set, vibrating membrane, asymptotic behaviour

Boella M.: Asymptotic Behavior of a Vibrating Membrane Model. Z. Anal. Anwend. 23 (2004), 39-66. doi: 10.4171/ZAA/1187