Competing effects of attraction vs. repulsion in chemotaxis

Youshan Tao, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

144 Citations (Scopus)

Abstract

We consider the attraction-repulsion chemotaxis system {equation presented} under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ Rnwith 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.
Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalMathematical Models and Methods in Applied Sciences
Volume23
Issue number1
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • Attraction-repulsion
  • Boundedness
  • Chemotaxis
  • Convergence
  • Entropy inequality
  • Stationary solutions

ASJC Scopus subject areas

  • Modelling and Simulation
  • Applied Mathematics

Cite this