Patterns in a generalized volume-filling chemotaxis model with cell proliferation

Manjun Ma, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


In this paper, we consider the following system [Equation presented here] which corresponds to the stationary system of a generalized volume-filling chemotaxis model with logistic source in a bounded domain in RN(N ≥ 1) with zero Neumann boundary conditions. Here the parameters D, χ, μ, ucare positive and α, β ∈ R, and ν denotes the outward unit normal vector of ∂Ω. With the priori positive lower- and upper-bound solutions derived by the Moser iteration technique and maximum principle, we apply the degree index theory in an annulus to show that if the chemotactic coefficient χ is suitably large, the system with α + β > 1 admits pattern solutions under certain conditions. Numerical simulations of the pattern formation are shown to illustrate the theoretical results and predict the interesting phenomenon for further studies.
Original languageEnglish
Pages (from-to)83-106
Number of pages24
JournalAnalysis and Applications
Issue number1
Publication statusPublished - 1 Jan 2017


  • Chemotaxis
  • degree index
  • nonconstant steady state
  • pattern formation
  • volume-filling effect

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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