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Regularity of solutions and approximate inertial manifolds for von Karman evolution equations

✍ Scribed by I. D. Chueshov

Publisher: John Wiley and Sons
Year: 1994
Tongue: English
Weight: 651 KB
Volume: 17
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670170902

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✦ Synopsis

Abstract

The necessary and sufficient conditions of regularity of solutions of von Karman evolution equations are derived. It is proved that a global attractor consists of smooth functions for these evolution equations. The results obtained are used to construct a family of approximate inertial manifolds. These finite dimensional manifolds approximate the global attractor and are determined by a simple iterative procedure. Their use makes it possible to suggest a new method of numerical investigation of long‐time behaviour and limit regimes of the equations in question. In particular, this method can be applied for studying a non‐linear flutter problem in real air space systems.

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