Abstract and Applied Analysis
Volume 2012 (2012), Article ID 272145, 20 pages
http://dx.doi.org/10.1155/2012/272145
Research Article

Regularity and Exponential Growth of Pullback Attractors for Semilinear Parabolic Equations Involving the Grushin Operator

Nguyen Dinh Binh

Faculty of Applied Mathematics and Informatics, Hanoi University of Technology, 1 Dai Co Viet, Hai Ba Trung, Hanoi, Vietnam

Received 24 November 2011; Accepted 28 December 2011

Academic Editor: Shaoyong Lai

Copyright © 2012 Nguyen Dinh Binh. 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

Considered here is the first initial boundary value problem for a semilinear degenerate parabolic equation involving the Grushin operator in a bounded domain Ω . We prove the regularity and exponential growth of a pullback attractor in the space 𝑆 2 0 ( Ω ) ∩ 𝐿 2 𝑝 − 2 ( Ω ) for the nonautonomous dynamical system associated to the problem. The obtained results seem to be optimal and, in particular, improve and extend some recent results on pullback attractors for reaction-diffusion equations in bounded domains.