Singularity formation in chemotaxis systems with volume-filling effect

Zhian Wang, Michael Winkler, Dariusz Wrzosek

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

A parabolic-elliptic model of chemotaxis which takes into account volume-filling effects is considered under the assumption that there is an a priori threshold for the cell density. For a wide range of nonlinear diffusion operators including singular and degenerate ones it is proved that if the taxis force is strong enough with respect to diffusion and the initial data are chosen properly then there exists a classical solution which reaches the threshold at the maximal time of its existence, no matter whether the latter is finite or infinite. Moreover, we prove that the threshold may even be reached in finite time provided the diffusion of cells is non-degenerate.
Original languageEnglish
Pages (from-to)3279-3297
Number of pages19
JournalNonlinearity
Volume24
Issue number12
DOIs
Publication statusPublished - 1 Dec 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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