Bulletin of the Australian Mathematical Society

Research Article

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

Joseph W.-H. Soa1 and Jianhong Wua2

a1 Department of Mathematics, University of Alberta, Edmonton Alberta, Canada T6G 2G1

a2 Department of Mathematics, York University, North York Ontario, Canada M3J IP3

Abstract

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.

(Received June 06 1991)