Convergence and approximation of inertial manifolds for evolution equations

Kazuo Kobayashi*, Reza Aftabizadeh

*この研究の対応する著者

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)1117-1134
ページ数18
ジャーナルDifferential and Integral Equations
8
5
出版ステータスPublished - 1995
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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