Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
J. J. L. Velázquez
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Source: Crossref
Published: Jan 1, 2004
DOI: 10.1137/s003613990343389x
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This paper continues the analysis started in the first part of this article (cf. [J. J. L. Velázquez, 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. Velázquez, 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.
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