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

Pages: 531 - 540, Issue Special, September 2007

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Nikos I. Karachalios - Department of Statistics and Actuarial Science, University of the Aegean, Karlovassi 83200, Samos, Greece (email)
Athanasios N Lyberopoulos - Department of Mathematics, University of Aegean, Karlovassi, GR 83200, Samos, Greece (email)

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.

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

Received: October 2006;      Revised: February 2007;      Published: September 2007.