Differential and Integral Equations

Convergence and approximation of inertial manifolds for evolution equations

Kazuo Kobayasi

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Abstract

This paper discusses the existence and the convergence of inertial manifolds for approximations to semi-linear evolution equations in Banach spaces. Our approximation considered here is closely related to Chernoff's product formulas. It is shown that the approximation possesses an inertial manifold and this manifold converges to the inertial manifold for the evolution equation. A "parabolic" version of Chernoff's lemma is established and used to prove the convergence theorems. As an application the schemes of "Crank-Nicholson type" are considered. Finally, the existence of inertial manifolds for the evolution equation is discussed under the condition that the approximations possess inertial manifolds.

Article information

Source
Differential Integral Equations, Volume 8, Number 5 (1995), 1117-1134.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056046

Mathematical Reviews number (MathSciNet)
MR1325548

Zentralblatt MATH identifier
0834.47037

Subjects
Primary: 34G20: Nonlinear equations [See also 47Hxx, 47Jxx]
Secondary: 34D45: Attractors [See also 37C70, 37D45] 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07] 47N20: Applications to differential and integral equations

Citation

Kobayasi, Kazuo. Convergence and approximation of inertial manifolds for evolution equations. Differential Integral Equations 8 (1995), no. 5, 1117--1134. https://projecteuclid.org/euclid.die/1369056046


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