Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Centre manifolds for partial differential equations with delays*

Xiaodong Lina1, 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

Synopsis

A centre manifold theory for reaction-diffusion equations with temporal delays is developed. Besides an existence proof, we also show that the equation on the centre manifold is a coupled system of scalar ordinary differential equations of higher order. As an illustration, this reduction procedure is applied to the Hutchinson equation with diffusion.

(Received July 17 1991)

(Revised November 26 1991)

Footnotes

* Research partially supported by the Natural Sciences and Engineering Research Council of Canada.