Global attractors for p-Laplacian equation ✩

The existence of a (L2(Ω),W 1,p 0 (Ω) ∩ Lq(Ω))-global attractor is proved for the p-Laplacian equation ut − div(|∇u|p−2∇u) + f (u) = g on a bounded domain Ω ⊂ Rn (n 3) with Dirichlet boundary condition, where p 2. The nonlinear term f is supposed to satisfy the polynomial growth condition of arbitrary order c1|u|q −k f (u)u c2|u|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. © 2006 Elsevier Inc. All rights reserved