# Convergence and approximation of inertial manifolds for evolution equations

4 引用 (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.

元の言語 English 1117-1134 18 Differential and Integral Equations 8 5 Published - 1995 Yes

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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

### これを引用

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

：: Differential and Integral Equations, 巻 8, 番号 5, 1995, p. 1117-1134.

Kobayashi, K & Aftabizadeh, R 1995, 'Convergence and approximation of inertial manifolds for evolution equations', Differential and Integral Equations, 巻. 8, 番号 5, pp. 1117-1134.
Kobayashi, Kazuo ; Aftabizadeh, Reza. / Convergence and approximation of inertial manifolds for evolution equations. ：: Differential and Integral Equations. 1995 ; 巻 8, 番号 5. pp. 1117-1134.
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