## Abstract and Applied Analysis

### Regularity of Global Attractor for the Reaction-Diffusion Equation

Hong Luo

#### Abstract

By using an iteration procedure, regularity estimates for the linear semigroups, and a classical existence theorem of global attractor, we prove that the reaction-diffusion equation possesses a global attractor in Sobolev space ${H}^{k}$ for all $k>0$, which attracts any bounded subset of ${H}^{k}$(${\Omega}$) in the ${H}^{k}$-norm.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 917190, 16 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.aaa/1355495777

Digital Object Identifier
doi:10.1155/2012/917190

Mathematical Reviews number (MathSciNet)
MR2947748

Zentralblatt MATH identifier
1246.35106

#### Citation

Luo, Hong. Regularity of Global Attractor for the Reaction-Diffusion Equation. Abstr. Appl. Anal. 2012 (2012), Article ID 917190, 16 pages. doi:10.1155/2012/917190. https://projecteuclid.org/euclid.aaa/1355495777

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