Convergence and approximation of inertial manifolds for evolution equations

Kazuo Kobayashi, Reza Aftabizadeh

Research output: Contribution to journalArticle

4 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1117-1134
Number of pages18
JournalDifferential and Integral Equations
Volume8
Issue number5
Publication statusPublished - 1995
Externally publishedYes

Fingerprint

Inertial Manifolds
Banach spaces
Evolution Equation
Approximation
Semilinear Evolution Equation
Product formula
Convergence Theorem
Lemma
Banach space
Converge

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Convergence and approximation of inertial manifolds for evolution equations. / Kobayashi, Kazuo; Aftabizadeh, Reza.

In: Differential and Integral Equations, Vol. 8, No. 5, 1995, p. 1117-1134.

Research output: Contribution to journalArticle

Kobayashi, Kazuo ; Aftabizadeh, Reza. / Convergence and approximation of inertial manifolds for evolution equations. In: Differential and Integral Equations. 1995 ; Vol. 8, No. 5. pp. 1117-1134.
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