Convergence and approximation of inertial manifolds for evolution equations

Kazuo Kobayashi, Reza Aftabizadeh

研究成果: Article

4 引用 (Scopus)

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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.

元の言語English
ページ(範囲)1117-1134
ページ数18
ジャーナルDifferential and Integral Equations
8
発行部数5
出版物ステータスPublished - 1995
外部発表Yes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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