Boundary Value Problems
Volume 2009 (2009), Article ID 563767, 17 pages
doi:10.1155/2009/563767

Existence of Global Attractors in Lp for m-Laplacian Parabolic Equation in RN

Abstract

We study the long-time behavior of solution for the m-Laplacian equation ut−div(|∇u|m−2∇u)+λ|u|m−2u+f(x,u)=g(x) in RN×R+, in which the nonlinear term f(x,u) is a function like f(x,u)=−h(x)|u|q−2u with h(x)≥0, 2≤q<m, or f(x,u)=a(x)|u|α−2u−h(x)|u|β−2u with a(x)≥h(x)≥0 and α>β≥m. We prove the existence of a global (L2(RN),Lp(RN))-attractor for any p>m.