Some new generalizations of inertial manifolds

Pages: 543 - 558, Volume 2, Issue 4, October 1996

doi:10.3934/dcds.1996.2.543       Abstract        Full Text (225.7K)

A. Debussche - Laboratoire d'Analyse Numérique et EDP, Unité de Recherche Associée 760, Université de Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France (email)
R. Temam - Laboratoire d'Analyse Numérique et EDP, Unité de Recherche Associée 760, Université de Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France (email)

Abstract: In this article we introduce two new generalizations of inertial manifolds. The first one is the concept of Inertial Manifold with Delay which may be physically more suitable than the usual concept of inertial manifold since it allows a certain delay time for the adjustment of the small scales to the large ones. We also introduce an invariant manifold which is the graph of a multivalued function and which exists under general conditions. We conjecture that, like an inertial manifold, this manifold attracts all orbits at an exponential rate.

Keywords:  inertial manifolds, invariant manifold.
Mathematics Subject Classification:  32Qxx.

Received: July 1996;      Published: July 1996.