Attractors in models of porous media flow

A constructive method is proposed for finding finite-dimensional submanifolds in the space of smooth functions that are invariant with respect to flows defined by evolutionary partial differential equations. Conditions for the stability of these submanifolds are obtained. Such submanifolds are const...

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Bibliographic Details
Published in:Doklady. Mathematics 2017, Vol.95 (1), p.72-75
Main Authors: Akhmetzyanov, A. V., Kushner, A. G., Lychagin, V. V.
Format: Article
Language:English
Subjects:
Manifolds (mathematics)
Mathematics
Mathematics and Statistics
Partial differential equations
Porous media
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Summary:A constructive method is proposed for finding finite-dimensional submanifolds in the space of smooth functions that are invariant with respect to flows defined by evolutionary partial differential equations. Conditions for the stability of these submanifolds are obtained. Such submanifolds are constructed for generalized Rapoport–Leas equations that arise in the theory of porous media flows.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562417010239