Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/33331
Title: Competing effects of attraction vs. repulsion in chemotaxis
Authors: Tao, Y
Wang, ZA 
Keywords: Attraction-repulsion
Boundedness
Chemotaxis
Convergence
Entropy inequality
Stationary solutions
Issue Date: 2013
Publisher: World Scientific
Source: Mathematical models and methods in applied sciences, 2013, v. 23, no. 1, p. 1-36 How to cite?
Journal: Mathematical models and methods in applied sciences 
Abstract: We consider the attraction-repulsion chemotaxis system {equation presented} under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ Rn with smooth boundary, where χ ≥ 0, ξ ≥ 0, α > 0, β > 0, γ > 0, δ > 0 and τ = 0, 1. We study the global solvability, boundedness, blow-up, existence of non-trivial stationary solutions and asymptotic behavior of the system for various ranges of parameter values. Particularly, we prove that the system with τ = 0 is globally well-posed in high dimensions if repulsion prevails over attraction in the sense that ξγ - χα > 0, and that the system with τ = 1 is globally well-posed in two dimensions if repulsion dominates over attraction in the sense that ξγ - χα > 0 and β = δ. Hence our results confirm that the attraction-repulsion is a plausible mechanism to regularize the classical Keller-Segel model whose solution may blow up in higher dimensions.
URI: http://hdl.handle.net/10397/33331
ISSN: 0218-2025
EISSN: 1793-6314
DOI: 10.1142/S0218202512500443
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