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

Francisco Balibrea; José Valero

doi:10.3934/dcds.1999.5.515

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1999, Volume 5, Issue 3: 515-528. Doi: 10.3934/dcds.1999.5.515

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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
2.
Fundación Universitaria San Pablo CEU, Elche-Elx

Received: April 30, 1997

Revised: December 31, 1998

Published: June 1999

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Abstract

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.

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Mathematics Subject Classification: 58F12, 58F39.

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