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

• Main Authors: Caisheng Chen, Lanfang Shi, Hui Wang
• Format: Article
• Language: English
• Published: SpringerOpen 2009-01-01
• Series: Boundary Value Problems
• Online Access: http://dx.doi.org/10.1155/2009/563767

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.