Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain

In this paper, we study the long-time behavior of solutions for the parabolic equation with nonlinear Laplacian principal part in Rn.We prove the existence of a global (L2(Rn), L∞(Rn))-attractor when n p and the existence of a global (L2(Rn), Lnp/(n−p)(Rn))-attractor when n>p.  2005 Elsevier Inc. All rights reserved.