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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$C^{1}$ approximations of inertial manifolds
via finite differences

Author: Kazuo Kobayasi
Journal: Proc. Amer. Math. Soc. 127 (1999), 1143-1150
MSC (1991): Primary 47H20; Secondary 35K55
MathSciNet review: 1610800
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Abstract: We construct an inertial manifold for the evolution equation as a limit of the inertial manifolds for the difference approximations of the Trotter-Kato type and show that this limit is taken in a $C^{1}$ topology.

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Kazuo Kobayasi
Affiliation: Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-Ku, Tokyo 169-8050, Japan

Keywords: Inertial manifold, long-time behavior, finite dynamical system, evolution equation
Received by editor(s): July 29, 1997
Additional Notes: This research was partially supported by Waseda University Grant for special Research Projects 97A-81.
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society