American Institute of Mathematical Sciences

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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

Nikos I. Karachalios 1, and  Athanasios N Lyberopoulos 2,

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.
Keywords: tail estimates, global attractor, asymptotically compact semiflow., Degenerate semilinear wave equation, energy equation method.
Mathematics Subject Classification: Primary: 35L15, 35Q40, 37L30; Secondary: 35Q60.
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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