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 |
|---|---|
| ページ（範囲） | 1117-1134 |
| ページ数 | 18 |
| ジャーナル | Differential and Integral Equations |
| 巻 | 8 |
| 発行部数 | 5 |
| 出版物ステータス | Published - 1995 |
| 外部発表 | Yes |
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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.研究成果: Article
}
TY - JOUR
T1 - Convergence and approximation of inertial manifolds for evolution equations
AU - Kobayashi, Kazuo
AU - Aftabizadeh, Reza
PY - 1995
Y1 - 1995
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84972513429&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84972513429&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84972513429
VL - 8
SP - 1117
EP - 1134
JO - Differential and Integral Equations
JF - Differential and Integral Equations
SN - 0893-4983
IS - 5
ER -