Reaction–Diffusion Problems on Time-Periodic Domains

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-23 DOI:10.1007/s10884-023-10308-9

Jane Allwright

引用次数: 1

Abstract

Abstract Reaction–diffusion equations are studied on bounded, time-periodic domains with zero Dirichlet boundary conditions. The long-time behaviour is shown to depend on the principal periodic eigenvalue of a transformed periodic-parabolic problem. We prove upper and lower bounds on this eigenvalue under a range of different assumptions on the domain, and apply them to examples. The principal eigenvalue is considered as a function of the frequency, and results are given regarding its behaviour in the small and large frequency limits. A monotonicity property with respect to frequency is also proven. A reaction–diffusion problem with a class of monostable nonlinearity is then studied on a periodic domain, and we prove convergence to either zero or a unique positive periodic solution.

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时间周期域上的反应扩散问题

研究了零Dirichlet边界条件下有界时间周期域上的反应扩散方程。证明了变换后的周期抛物型问题的长时性依赖于主周期特征值。在定义域上不同的假设条件下，证明了该特征值的上界和下界，并将其应用到实例中。将主特征值视为频率的函数，并给出了主特征值在小频率和大频率极限下的特性。并证明了关于频率的单调性。在周期域上研究了一类单稳定非线性反应扩散问题，并证明了该问题收敛于零或收敛于唯一的正周期解。

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.