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

Nikos I. Karachalios; Athanasios N Lyberopoulos

doi:10.3934/proc.2007.2007.531

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2007, Volume 2007: 531-540. Doi: 10.3934/proc.2007.2007.531 open access

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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
2.
Department of Mathematics, University of Aegean, Karlovassi, GR 83200, Samos

Received: September 30, 2006

Revised: January 31, 2007

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L15, 35Q40, 37L30; Secondary: 35Q60 .

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