Invariant Manifolds for a PDE-ODE Coupled System

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-28 DOI:10.1007/s10884-024-10353-y

Xingjie Yan, Kun Yin, Xin-Guang Yang, Alain Miranville

引用次数: 0

Abstract

The aim of this paper is to construct invariant manifolds for a coupled system, consisting of a parabolic equation and a second-order ordinary differential equation, set on \(\mathbb {T}^3\) and subject to periodic boundary conditions. Notably, the “spectral gap condition" does not hold for the system under consideration, leading to the use of the spatial averaging principle, together with the graph transform method. This approach facilitates the construction of the relevant invariant manifold, characterized by attributes such as Lipschitz continuity, local invariance, infinite dimensionality, and exponential tracking, thus mirroring the properties traditionally associated with a classical global manifold.

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PDE-ODE 耦合系统的不变量频域

本文的目的是为一个耦合系统构建不变流形，该系统由抛物方程和二阶常微分方程组成，设置在 \(\mathbb {T}^3\) 上，并受周期性边界条件的限制。值得注意的是，"频谱间隙条件 "在所考虑的系统中并不成立，因此需要使用空间平均原理和图变换方法。这种方法有助于构建相关的不变量流形，其特征包括 Lipschitz 连续性、局部不变性、无限维度和指数跟踪等属性，从而反映了传统上与经典全局流形相关的属性。

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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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.