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1995 Convergence and approximation of inertial manifolds for evolution equations
Kazuo Kobayasi
Differential Integral Equations 8(5): 1117-1134 (1995). DOI: 10.57262/die/1369056046


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.


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Kazuo Kobayasi. "Convergence and approximation of inertial manifolds for evolution equations." Differential Integral Equations 8 (5) 1117 - 1134, 1995.


Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0834.47037
MathSciNet: MR1325548
Digital Object Identifier: 10.57262/die/1369056046

Primary: 34G20
Secondary: 34D45 , 47H20 , 47N20

Rights: Copyright © 1995 Khayyam Publishing, Inc.


Vol.8 • No. 5 • 1995
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