Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/65554
Title: Patterns in a generalized volume-filling chemotaxis model with cell proliferation
Authors: Ma, M
Wang, Z
Keywords: Chemotaxis
degree index
Nonconstant steady state
Pattern formation
Volume-filling effect
Issue Date: 2017
Publisher: World Scientific
Source: Analysis and applications, 2017, v. 15, no. 1, p. 83-106 How to cite?
Journal: Analysis and applications 
Abstract: 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, uc are 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.
URI: http://hdl.handle.net/10397/65554
ISSN: 0219-5305
EISSN: 1793-6861
DOI: 10.1142/S0219530515500220
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