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C1Approximations of Inertial Manifolds for Dissipative Nonlinear Equations

โœ Scribed by Don A. Jones; Edriss S. Titi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
714 KB
Volume
127
Category
Article
ISSN
0022-0396

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โœฆ Synopsis

In this paper we study a class of nonlinear dissipative partial differential equations that have inertial manifolds. This means that the long-time behavior is equivalent to a certain finite system of ordinary differential equations. We investigate ways in which these finite systems can be approximated in the C 1 sense. Geometrically this may be interpreted as constructing manifolds in phase space that are C 1 close to the inertial manifold of the partial differential equation. Under such approximations the invariant hyperbolic sets of the global attractor persist.

๐Ÿ“œ SIMILAR VOLUMES

Regularity of solutions and approximate
Regularity of solutions and approximate inertial manifolds for von Karman evolution equations
โœ I. D. Chueshov ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 651 KB

## 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