Abstract and Applied Analysis
Volume 2012 (2012), Article ID 541426, 18 pages
http://dx.doi.org/10.1155/2012/541426
Research Article

Dimension Estimate for the Global Attractor of an Evolution Equation

Renato Colucci and Gerardo R. Chacón

Departamento de Matemática, Pontificia Universidad Javeriana, Carrera 7 No. 43-82, Bogotá, Colombia

Received 29 September 2011; Accepted 13 December 2011

Academic Editor: Juan J. Nieto

Copyright © 2012 Renato Colucci and Gerardo R. Chacón. 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 estimate the dimension of the global attractor of an evolution equation by the study of the evolution of the n-dimensional volumes under the flow. We compare these results with the estimate of the dimension of the inertial manifold.