Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding

T. Hillen, K. Painter

Research output: Contribution to journalArticlepeer-review

244 Citations (Scopus)


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. © 2001 Academic Press.

Original languageEnglish
Pages (from-to)280-301
Number of pages22
JournalAdvances in Applied Mathematics
Issue number4
Publication statusPublished - May 2001


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