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

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.