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POINT DYNAMICS IN A SINGULAR LIMIT OF THE KELLER--SEGEL MODEL 2: FORMATION OF THE CONCENTRATION REGIONS.
- Source :
-
SIAM Journal on Applied Mathematics . 2004, Vol. 64 Issue 4, p1224-1248. 25p. - Publication Year :
- 2004
-
Abstract
- This paper continues the analysis started in the first part of this article (cf. [J. J. L. Velázquez, <em>SIAM J.</em> 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, <em>SIAM J.</em> 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361399
- Volume :
- 64
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 14082927
- Full Text :
- https://doi.org/10.1137/S003613990343389X