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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 541426, 18 pages
doi:10.1155/2012/541426
Research Article
Dimension Estimate for the Global Attractor of an Evolution Equation
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.