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

We study the long-time behavior of solution for the m -Laplacian equation ut -div(|∇u|m-2 ∇u)+λ|u|m-2 u+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-2 u with h(x)≥0 , 2≤q<m , or f(x,u)=a(x)|u|α-2 u-h(x)|u|β-2 u with a(x)≥h(x)≥0 and α>β≥m . We p...

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Bibliographic Details
Published inBoundary value problems Vol. 2009
Main Authors Chen, Caisheng, Shi, Lanfang, Wang, Hui
Format Journal Article
LanguageEnglish
Published New York Hindawi Limited 01.01.2009
SpringerOpen
Subjects
Boundary value problems
Estimates
Mathematics
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Summary:We study the long-time behavior of solution for the m -Laplacian equation ut -div(|∇u|m-2 ∇u)+λ|u|m-2 u+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-2 u with h(x)≥0 , 2≤q<m , or f(x,u)=a(x)|u|α-2 u-h(x)|u|β-2 u 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 .
ISSN:1687-2762
1687-2770
DOI:10.1155/2009/563767