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Topological dimensions of global attractors for semilinear PDE's with delays

Published online by Cambridge University Press:  17 April 2009

Joseph W.-H. So  and
Jianhong Wu
Joseph W.-H. So
Affiliation:
Department of Mathematics, University of Alberta, Edmonton Alberta, CanadaT6G 2G1
Jianhong Wu
Affiliation:
Department of Mathematics, York University, North York Ontario, CanadaM3J IP3
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Abstract

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An estimate is obtained on the Hausdorff and fractal dimensions of global attractors of semilinear partial differential equations with delay: ẋ(t) = Ax(t) + f(xt). The method employed is to associate such an equation with a nonlinear semigroup on a product space and then appeal to the upper estimate due to Constantin, Foias and Teman on topological dimensions of global attractors for general nonlinear dynamical systems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 407 - 422
Copyright
Copyright © Australian Mathematical Society 1991

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