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

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

Caisheng Chen,1 Lanfang Shi,1,2 and Hui Wang1,3

1Department of Mathematics, Hohai University, Nanjing 210098, Jiangsu, China
2College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
3Department of Mathematics, Ili Normal University, Yining 835000, Xinjiang, China

Received 4 April 2009; Revised 9 July 2009; Accepted 24 July 2009

Academic Editor: Zhitao Zhang

Copyright © 2009 Caisheng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.