Global attractors for p-Laplacian equation

The existence of a (L-2(Omega), W-0(1,p)(Omega) boolean AND L-q(Omega))-global attractor is proved for the p-Laplacian equation u(t) - div(vertical bar del u vertical bar(p-2)del u) + f(u) =g on abounded domain Omega subset of R-n (n >= 3) with Dirichlet boundary condition, where p >= 2. The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c(1)vertical bar u vertical bar(q) - k <= f (u)u <= c(2)vertical bar u vertical bar(q) + k and f'(u) >= -l, where q >= 2 is arbitrary. There is no other restriction on p and q. The asymptotic compactness of the corresponding semigroup is proved by using a new a priori estimate method, called asymptotic a priori estimate. (c) 2006 Elsevier Inc. All rights reserved.