Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 989475, 10 pages
http://dx.doi.org/10.1155/2013/989475
Research Article

Asymptotic Smoothing and Global Attractors for a Class of Nonlinear Evolution Equations

1School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha 410004, China
2Hunan Provincial Center for Disease Control and Prevention, Changsha, Hunan 410005, China

Received 31 March 2013; Accepted 24 April 2013

Academic Editors: S. Liu and W. Shen

Copyright © 2013 Yongqin Xie 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 prove the asymptotic regularity of global solutions for a class of semilinear evolution equations in . Moreover, we study the long-time behavior of the solutions. It is proved that, under the natural assumptions, these equations possess the compact attractor which is bounded in , where the nonlinear term satisfies a critical exponential growth condition.