Differential and Integral Equations

Steady approximate inertial manifolds of exponential order for semilinear parabolic equations

Alexander V. Rezounenko

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Abstract

The long time behavior of a class of autonomous semilinear parabolic equations is investigated. We employ the recently introduced concept of Inertial Manifold with Delay to construct a new family of approximate inertial manifolds (AIM) of an exponential order. These AIMs contain all steady states of the system under consideration.

Article information

Source
Differential Integral Equations, Volume 15, Number 11 (2002), 1345-1356.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060726

Mathematical Reviews number (MathSciNet)
MR1920691

Zentralblatt MATH identifier
1161.35427

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35B42: Inertial manifolds 37L25: Inertial manifolds and other invariant attracting sets 37L65: Special approximation methods (nonlinear Galerkin, etc.)

Citation

Rezounenko, Alexander V. Steady approximate inertial manifolds of exponential order for semilinear parabolic equations. Differential Integral Equations 15 (2002), no. 11, 1345--1356. https://projecteuclid.org/euclid.die/1356060726


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