Global attractors for p-Laplacian equation

AbstractThe existence of a (L2(Ω),W01,p(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