非线性SobolevGalpern方程的近似惯性流形

数学物理学报 ›› 2004, Vol. 24 ›› Issue (1): 105-115.

非线性SobolevGalpern方程的近似惯性流形

尚亚东, 郭柏灵

广州大学数学系广州 510405 北京应用物理与计算数学研究所非线性研究中心北京 100088

出版日期:2004-02-25 发布日期:2004-02-25
基金资助:
国家自然科学基金(10271034)资助

Approximate Inertial Manifolds for the Nonlinear Sobolev Galpern Equations

SHANG Y-Dong, GUO Bo-Ling

Online:2004-02-25 Published:2004-02-25
Supported by:
国家自然科学基金(10271034)资助

摘要/Abstract

摘要：

近似惯性流形概念与耗散偏微分方程的长时间行为研究有关, 该文对非线性Sobolev Galpern方程构造了两个近似惯性流形. 证明了非平滑近似惯性流形Σ和平滑近似惯性流形Σ_0=P_mH对整体吸引子有相同的逼近阶数.

关键词: 非线性Sobolev Galpern方程, 长时间行为, 近似惯性流形

Abstract:

The concept of approximate inertial manifold is related to the study of the long time behavior of dissiputive partial differential equations. In the present paper, the authors construct two approximate inertial manifolds for the nonlinear Sobolev Galpern equations. The authors show that the non flat approximate inertial manifold Σ and the flat approximate inertial manifold Σ_0=P_mH have the same order of approximation to the global attractor.

Key words: Nonlinear Sobolev Galpern equations, Long time behavior, Approximate inertial manifolds.

中图分类号:

35B40

尚亚东, 郭柏灵. 非线性SobolevGalpern方程的近似惯性流形[J]. 数学物理学报, 2004, 24(1): 105-115.

SHANG Y-Dong, GUO Bo-Ling. Approximate Inertial Manifolds for the Nonlinear Sobolev Galpern Equations[J]. Acta mathematica scientia,Series A, 2004, 24(1): 105-115.

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