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October  2001, 7(4): 719-735. doi: 10.3934/dcds.2001.7.719

Attractors for semilinear strongly damped wave equations on $\mathbb R^3$

Veronica Belleri 1, and  Vittorino Pata 2,

1. 

Dipartimento di Matematica, Università Cattolica del S. Cuore, Brescia, Italy
2. 

Dipartimento di Matematica "F. Brioschi", Politecnico di Milano

Received  December 2000 Revised  February 2001 Published  July 2001

A strongly damped semilinear wave equation on the whole space is considered. Existence and uniqueness results are provided, together with the existence of an absorbing set, which is uniform as the external force is allowed to run in a certain functional set. In the autonomous case, the equation is shown to possess a universal attractor.
Keywords: uniform absorbing sets, Kuratowski measure of non-compactness, universal attractors., Strongly damped wave equations.
Mathematics Subject Classification: 35B40, 35L05, 58F1.
Citation: Veronica Belleri, Vittorino Pata. Attractors for semilinear strongly damped wave equations on $\mathbb R^3$. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 719-735. doi: 10.3934/dcds.2001.7.719
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