Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
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DOI：
10.1137/s003613990343389x
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发表时间：
2004
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影响因子：
--
通讯作者：
J. Velázquez
中科院分区：
文献类型：
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作者：
J. Velázquez
本文继续了本文第一部分开始的分析（参见第二部分）。[J. J. L. Velazquez，SIAM J.应用数学，64（2004），pp. 1198- 1223]）。有人看到那里，使用匹配渐近的方法，一个正规化版本的凯勒-西格尔系统承认，为一个合适的渐近极限，解决方案与一些地区的高浓度的细胞密度。本文考虑了极限问题的爆破现象与[J，J，L。Velazquez，SIAM J.应用数学，64（2004），pp. 1198- 1223]。特别是，本文分析了在凯勒-西格尔系统中引入的正则化停止聚集过程并产生浓度区域的形成的精确方式。
This paper continues the analysis started in the first part of this article (cf. [J. J. L. Velazquez, SIAM J. Appl. Math., 64 (2004), pp. 1198--1223]). It was seen there, using the method of matched asymptotics, that a regularized version of the Keller--Segel system admits, for a suitable asymptotic limit, solutions with some regions of high concentrations for the cell density. This paper considers the relation between the phenomenon of blow-up for the limit problem and the dynamics of the concentration regions described in [J. J. L. Velazquez, SIAM J. Appl. Math., 64 (2004), pp. 1198--1223]. In particular, this paper analyzes the precise way in which the regularization introduced in the Keller--Segel system stops the aggregation process and yields the formation of concentration regions.