Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-07 DOI:10.1007/s10884-024-10380-9

Nicole Gauss, Anna Logioti, Guido Schneider, Dominik Zimmermann

引用次数: 0

Abstract

We are interested in reaction–diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number \( k = 0 \). With the help of a multiple scaling perturbation ansatz a Ginzburg–Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction–diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions.

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具有守恒定律的长波霍普夫不稳定空间扩展系统的全局存在性

我们对具有守恒定律的反应-扩散系统感兴趣，该系统在空间波数 \( k = 0 \)处出现霍普夫分岔。在多重缩放扰动解析的帮助下，一个与标量守恒定律耦合的金兹堡-朗道方程可以被推导为一个振幅系统，用于近似描述原始反应-扩散系统在第一个不稳定性附近的动力学。我们利用振幅系统证明，对于在大空间区间上具有周期性边界条件的原始系统，从弱不稳定基态的一个小邻域开始，所有解都是全局存在的。

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.