Existence of Multi-spikes in the Keller-Segel model with Logistic Growth

IF 3.6 1区 数学 Q1 MATHEMATICS, APPLIED
Fanze Kong, Juncheng Wei, Liangshun Xu
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引用次数: 3

Abstract

The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex non-trivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we employ the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.
具有Logistic增长的Keller-Segel模型中多尖峰的存在性
Keller–Segel模型是一种描述趋化机制的范式,它对单细胞和多细胞生物的生理和病理活动起着至关重要的作用。最有趣的变体之一是具有内在增长的耦合系统,它允许许多复杂的非平凡模式。本文致力于构造具有二维逻辑源的Keller–Segel模型的多尖峰解。假设化学吸引率较大,我们将内外胶合方案应用于非局部交叉扩散系统,并证明了多个边界和内部尖峰的存在。数值模拟是为了突出我们的理论结果。
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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来源期刊
CiteScore
6.30
自引率
17.10%
发文量
61
审稿时长
1 months
期刊介绍: The purpose of this journal is to provide a medium of exchange for scientists engaged in applied sciences (physics, mathematical physics, natural, and technological sciences) where there exists a non-trivial interplay between mathematics, mathematical modelling of real systems and mathematical and computer methods oriented towards the qualitative and quantitative analysis of real physical systems. The principal areas of interest of this journal are the following: 1.Mathematical modelling of systems in applied sciences; 2.Mathematical methods for the qualitative and quantitative analysis of models of mathematical physics and technological sciences; 3.Numerical and computer treatment of mathematical models or real systems. Special attention will be paid to the analysis of nonlinearities and stochastic aspects. Within the above limitation, scientists in all fields which employ mathematics are encouraged to submit research and review papers to the journal. Both theoretical and applied papers will be considered for publication. High quality, novelty of the content and potential for the applications to modern problems in applied sciences and technology will be the guidelines for the selection of papers to be published in the journal. This journal publishes only articles with original and innovative contents. Book reviews, announcements and tutorial articles will be featured occasionally.
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