具有非均匀翻滚内核的运行和翻滚方程的平衡趋势

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED Acta Applicandae Mathematicae Pub Date : 2024-05-14 DOI:10.1007/s10440-024-00657-y
Josephine Evans, Havva Yoldaş
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引用次数: 0

摘要

我们研究了运行和翻滚模型的长期行为,该模型是一个描述细菌在化学刺激作用下运动的动力学-传输方程。实验表明,非均匀翻滚核与文献中广泛考虑的均匀翻滚核不同,它与物理相关,可以降低数学分析的复杂性。我们考虑了两种情况:(i) 翻滚核取决于翻滚前速度和翻滚后速度之间的夹角;(ii) 速度空间是无界的,翻滚后速度遵循麦克斯韦速度分布。我们证明,对于任何概率度量初始数据,细菌的概率密度分布都会以明确的收敛率((i)为指数收敛率,(ii)为代数收敛率)收敛到平衡分布。据我们所知,我们的结果是关于具有非均匀翻滚核的运行和翻滚方程的长期行为的第一个结果。
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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Trend to Equilibrium for Run and Tumble Equations with Non-uniform Tumbling Kernels

We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels.

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来源期刊
Acta Applicandae Mathematicae
Acta Applicandae Mathematicae 数学-应用数学
CiteScore
2.80
自引率
6.20%
发文量
77
审稿时长
16.2 months
期刊介绍: Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.
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