A sufficient condition for the existence of approximate inertial manifolds containing the global attractor

Rezounenko, Alexander

Comptes Rendus. Mathématique, Tome 334 (2002) no. 11, pp. 1015-1020.

Utilisant le récent concept de variété inertielle avec retard, nous présentons une nouvelle méthode de construction de variétés inertielles approchées. Dans le cas où l'attracteur global peut être plongé dans une variété C² de dimension finie, nous construisons une variété inertielle approchée de la même dimension contenant l'attracteur.

Using the recently introduced concept of inertial manifold with delay we present a new method of construction of approximate inertial manifolds (AIMs). In the case when the global attractor can be embedded into a finite-dimensional C²-manifold we construct AIMs of the same dimension which contain the attractor.

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