# American Institute of Mathematical Sciences

2007, 2007(Special): 531-540. doi: 10.3934/proc.2007.2007.531

## On the dynamics of a degenerate damped semilinear wave equation in \mathbb{R}^N : the non-compact case

 1 Department of Statistics and Actuarial Science, University of the Aegean, Karlovassi 83200, Samos, Greece 2 Department of Mathematics, University of Aegean, Karlovassi, GR 83200, Samos, Greece

Received  October 2006 Revised  February 2007 Published  September 2007

We show the existence of a global attractor for a degenerate, linearly damped, semilinear wave equation in $mathbb{R}^N$ under a new condition concerning a variable non-negative diffusivity. In particular, we show the asymptotic compactness of the induced semiflow by combining the energy equation method with appropriate tail estimates.
Citation: Nikos I. Karachalios, Athanasios N Lyberopoulos. On the dynamics of a degenerate damped semilinear wave equation in \mathbb{R}^N : the non-compact case. Conference Publications, 2007, 2007 (Special) : 531-540. doi: 10.3934/proc.2007.2007.531
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