薄域上耗散动力系统不变量的逼近

IF 1.1 2区数学 Q1 MATHEMATICS Banach Journal of Mathematical Analysis 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

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.

期刊最新文献

On embeddings in the intersection $$X\cap L_{\infty }$$ 2-Rotund norms for unconditional and symmetric sequence spaces Compactness of averaging operators on Banach function spaces Approximation of invariant measures of dissipative dynamical systems on thin domains Generalized interpolation for type 1 subdiagonal algebras