Asymptotic Behavior of a Class of Degenerate Parabolic Equations

Abstract

We investigate the asymptotic behavior of solutions of a class of degenerate parabolic equations in a bounded domain $\Omega \subset {ℝ}^n$ ($n⩾2$) with a polynomial growth nonlinearity of arbitrary order. The existence of global attractors is proved in $L^2(\Omega )$, $L^p(\Omega )$, and $H_0^{1,a}(\Omega )$, respectively, when $H_0^{1,a}(\Omega )$ can be just compactly embedded into $L^r(\Omega )$ () but not $L^2(\Omega )$.