Suppression of blowup by slightly superlinear degradation in a parabolic–elliptic Keller–Segel system with signal-dependent motility

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-17 DOI:10.1016/j.nonrwa.2024.104190

Aijing Lu, Jie Jiang

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Abstract

In this paper, we consider an initial–Neumann boundary value problem for a parabolic–elliptic Keller–Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension $N \geq 2$ . In the current work, when $N \leq 3$ , we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order $s log s$ , unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works (Fujie and Jiang, 2020; Lyu and Wang, 2023) which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively.

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在抛物线-椭圆形凯勒-西格尔系统中通过轻微超线性退化抑制炸裂，该系统的运动依赖于信号

在本文中，我们考虑了一个抛物线-椭圆 Keller-Segel 系统的初始-Neumann 边界值问题，该系统具有与信号相关的运动性和一个源项。以往的研究已经严格证明，当维数 N≥2 时，该系统的无源版本会出现无限时炸毁现象。在当前的研究中，当 N≤3 时，我们建立了全局经典解的均匀有界性，并增加了一个源项，该源项涉及对密度的轻微超线性退化效应，最大增长阶数为 slogs，从而揭示了一种充分的炸毁抑制机制。与局限于单调非递增情况的近期研究（Fujie 和 Jiang，2020；Lyu 和 Wang，2023）相比，我们研究中考虑的运动函数采用了一种相当通用的形式。我们证明的基石在于推导出系统第二分量的上界和类似熵的估计值，这分别是通过刁钻比较技巧和能量方法实现的。

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.