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October  1999, 5(4): 813-824. doi: 10.3934/dcds.1999.5.813

Inertial manifolds with and without delay

James C. Robinson 1,

1. 

Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Received  December 1997 Revised  October 1998 Published  July 1999

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.
Keywords: integral manifold., inertial manifold with delay, Inertial manifold, multi-valued inertial manifold.
Mathematics Subject Classification: 35B40, 35K5.
Citation: James C. Robinson. Inertial manifolds with and without delay. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 813-824. doi: 10.3934/dcds.1999.5.813
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