Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding

In this paper we study a version of the Keller–Segel model where the chemotactic cross-diffusion depends on both the external signal and the local population density. A parabolic quasi-linear strongly coupled system follows. By incorporation of a population-sensing (or “quorum-sensing”) mechanism, w...

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Bibliographic Details
Published in:Advances in applied mathematics 2001-05, Vol.26 (4), p.280-301
Main Authors: Hillen, T., Painter, K.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Partial differential equations
Sciences and techniques of general use
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Summary:In this paper we study a version of the Keller–Segel model where the chemotactic cross-diffusion depends on both the external signal and the local population density. A parabolic quasi-linear strongly coupled system follows. By incorporation of a population-sensing (or “quorum-sensing”) mechanism, we assume that the chemotactic response is switched off at high cell densities. The response to high population densities prevents overcrowding, and we prove local and global existence in time of classical solutions. Numerical simulations show interesting phenomena of pattern formation and formation of stable aggregates. We discuss the results with respect to previous analytical results on the Keller–Segel model.
ISSN:0196-8858
1090-2074
DOI:10.1006/aama.2001.0721