薄域上耗散动力系统不变量的逼近

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-11 DOI:10.1007/s43037-024-00384-4

Dingshi Li, Ran Li

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引用次数: 0

摘要

本文提出了一种抽象方法，用以证明薄域上耗散动力系统不变度量的上半连续性。提出的抽象方法可用于许多物理系统。例如，我们考虑薄域上的反应扩散方程。为此，我们首先证明了方程在 \(\mathbb {R}^{n+1}\) 有界域中的不变度量的存在，这个有界域可以看作是 \(\mathbb {R}^{n\) 有界域的扰动。然后我们证明，当薄域坍缩时，扰动系统不变度量的任何极限一定是极限系统的不变度量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Approximation of invariant measures of dissipative dynamical systems on thin domains

An abstract method is presented to show that upper semicontinuity of invariant measures of dissipative dynamical systems on thin domains. The abstract method presented can be used to many physical systems. As an example, we consider reaction-diffusion equations on thin domains. To this end, we first show the existence of invariant measures of the equations in a bounded domain in \(\mathbb {R}^{n+1}\) which can be viewed as a perturbation of a bounded domain in \(\mathbb {R}^n\). We then prove that any limit of invariant measures of the perturbed systems must be an invariant measure of the limiting system when the thin domains collapses.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.