Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 204270, 14 pages
http://dx.doi.org/10.1155/2013/204270
Research Article

Asymptotic Behavior for a Class of Nonclassical Parabolic Equations

School of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received 18 May 2013; Accepted 18 June 2013

Academic Editors: Y.-K. Chang, X. Xue, and K.-V. Yuen

Copyright © 2013 Yanjun Zhang and Qiaozhen Ma. 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

This paper is devoted to the qualitative analysis of a class of nonclassical parabolic equations with critical nonlinearity, where and are two parameters. Firstly, we establish some uniform decay estimates for the solutions of the problem for , which are independent of the parameter . Secondly, some uniformly (with respect to ) asymptotic regularity about the solutions has been established for , which shows that the solutions are exponentially approaching a more regular, fixed subset uniformly (with respect to ). Finally, as an application of this regularity result, a family of finite dimensional exponential attractors has been constructed. Moreover, to characterize the relation with the reaction diffusion equation ( ), the upper semicontinuity, at , of the global attractors has been proved.