Classical solutions and pattern formation for a volume filling chemotaxis model

Zhian Wang, Thomas Hillen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

102 Citations (Scopus)


We establish the global existence of classical solutions to a generalized chemotaxis model, which includes the volume filling effect expressed through a nonlinear squeezing probability. This novel choice of squeezing probability reflects the elastic properties of cells. Necessary and sufficient conditions for spatial pattern formation are given and the underlying bifurcations are analyzed. In numerical simulations, the complex dynamics of merging and emerging patterns are shown for zero cell kinetics and nonzero cell kinetics, respectively. We conclude that the emerging process of pattern formation is due to cell growth.
Original languageEnglish
Article number037108
Issue number3
Publication statusPublished - 1 Jan 2007
Externally publishedYes

ASJC Scopus subject areas

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


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