Paper Info
Title
Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
Abstract
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.
Year
DOI
Venue
2004
10.1137/S003613990343389X
SIAM JOURNAL ON APPLIED MATHEMATICS
Keywords
Field
DocType
chemotaxis,singular perturbations,matched asymptotics
Mathematical optimization,Mathematical analysis,Cell density,Regularization (mathematics),Asymptotic analysis,Mathematics
Journal
Volume
Issue
ISSN
64
4
0036-1399
Citations 
PageRank 
References 
1
0.41
0
Authors
1
Name
Order
Citations
PageRank
J. J. L. Velázquez1138.41