Inertial manifolds with and without delay

James C. Robinson

doi:10.3934/dcds.1999.5.813

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1999, Volume 5, Issue 4: 813-824. Doi: 10.3934/dcds.1999.5.813

This issue Previous Article Large deviations in expanding random dynamical systems Next Article Global smooth solutions of the complex Ginzburg-Landau equation and their dynamical properties

Inertial manifolds with and without delay

James C. Robinson^1,

1.
Mathematics Institute, University of Warwick, Coventry CV4 7AL

Received: December 1997

Revised: October 1998

Published: October 1999

Abstract / Introduction Related Papers Cited by

Abstract

This article discusses the relationship between the inertial manifolds "with delay" introduced by Debussche & Temam, and the standard definition. In particular, the "multi-valued" manifold of the same paper is shown to arise naturally from the manifolds "with delay" when considering issues of convergence as the delay time tends to infinity. This leads to a new characterisation of the multi-valued manifold, which allows a fuller understanding of its structure.

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Mathematics Subject Classification: 35B40, 35K55.

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