时滞惯性流形及近似时滞惯性流形族  

IMD and a Family of Approximate IMDs

作　　者：李开泰[1] 侯延仁[1] 

机构地区：[1]西安交通大学理学院,陕西西安710049

出　　处：《数学学报（中文版）》2000年第3期435-444,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金!(19671067);国家重大基础研究项目!(G1999032801)

摘　　要：时滞惯性流形是对耗散系统惯性流形、近似惯性流形的最新发展，它基于对 大小涡分量间相互作用更细致的观察，即改变了惯性流形和近似惯性流形方法中大小 涡分量间相互作用为瞬时行为的隐含假定，而认为这种作用与系统的历史相关的．本 文结出了一类耗散系统时滞惯性流形的存在性证明，由于其存在性不需要“谱间隔条 件”保证，因而时滞惯性流形是广泛存在的．随后我们引出了一类离散的时滞惯性流 形，并在此基础上构造了一种近似时滞惯性流形族，分别给出了它们近似时滞惯性流 形的误差估计，结果显示这种新方法为构造稳定和高精度的算法提供了可能．Inertial Manifold with Delay (IMD) is the recent development of the Inerial Manifold (IM) and Approximate Inertial Manifold (AIM) for the dissipative systems, which is based on the more precise observation of the interaction between large and small eddies, that is we believe this kind of interaction is related with the history of the system instead of implicitly regarding it is instantaneous as in IM and AIM. In this paper, we present a proof of the existence of IMD with respect to a certain sort of dissipative system. Becasue the so-called 'spectral gap condition' is hot necessary for the existence of IMD, it exists widely. Then we introduce a kind of discrete IMD and construct a family of IMD. Their error estimations for approximating IMD show that this kind of method can provide a possible way to construct stable and accurate algorithms.

关 键 词：耗散系统 近似惯性流形 时滞惯性流形 发展方程 

分 类 号：O175.29[理学—数学] O241.82[理学—基础数学]