On dimension of attractors of differential inclusions and reaction-diffussion equations

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July 1999, 5(3): 515-528. doi: 10.3934/dcds.1999.5.515

On dimension of attractors of differential inclusions and reaction-diffussion equations

Francisco Balibrea ^1, and José Valero ^2,

1.	Departamento de Matemáticas, Universidad de Murcia, Spain
2.	Fundación Universitaria San Pablo CEU, Elche-Elx, Spain

Received May 1997 Revised January 1999 Published May 1999

Abstract
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In this paper we improve a general theorem of O.A. Ladyzhenskaya on the dimension of compact invariant sets in Hilbert spaces. Then we use this result to prove that the Hausdorff and fractal dimensions of global compact attractors of differential inclusions and reaction-diffusion equations are finite.

Keywords: Attractor, Hausdorff dimension, fractal dimension..

Mathematics Subject Classification: 58F12, 58F3.

Citation: Francisco Balibrea, José Valero. On dimension of attractors of differential inclusions and reaction-diffussion equations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 515-528. doi: 10.3934/dcds.1999.5.515

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