Open Access

Existence of Global Attractors in https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq1_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq2_HTML.gif -Laplacian Parabolic Equation in https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq3_HTML.gif

Boundary Value Problems20092009:563767

DOI: 10.1155/2009/563767

Received: 4 April 2009

Accepted: 24 July 2009

Published: 26 August 2009

Abstract

We study the long-time behavior of solution for the https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq4_HTML.gif -Laplacian equation https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq5_HTML.gif in https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq6_HTML.gif , in which the nonlinear term https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq7_HTML.gif is a function like https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq8_HTML.gif with https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq9_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq10_HTML.gif , or https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq11_HTML.gif with https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq12_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq13_HTML.gif . We prove the existence of a global https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq14_HTML.gif -attractor for any https://static-content.springer.com/image/art%3A10.1155%2F2009%2F563767/MediaObjects/13661_2009_Article_859_IEq15_HTML.gif .

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Authors’ Affiliations

(1)
Department of Mathematics, Hohai University
(2)
College of Mathematics and Physics, Nanjing University of Information Science and Technology
(3)
Department of Mathematics, Ili Normal University

Copyright

© Caisheng Chen et al. 2009

This article is published under license to BioMed Central Ltd. 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.