Comptes Rendus
A sufficient condition for the existence of approximate inertial manifolds containing the global attractor
Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 1015-1020.

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.

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.

Received:
Revised:
Published online:
DOI: 10.1016/S1631-073X(02)02385-3

Alexander Rezounenko 1

1 Department of Mechanics and Mathematics, Kharkov University, 4 Svobody square, Kharkov 61077, Ukraine
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Alexander Rezounenko. A sufficient condition for the existence of approximate inertial manifolds containing the global attractor. Comptes Rendus. Mathématique, Volume 334 (2002) no. 11, pp. 1015-1020. doi : 10.1016/S1631-073X(02)02385-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02385-3/

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For my parents Vyacheslav and Larisa.

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