Steadily propagating waves of a chemotaxis model

Tong Li, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

38 Citations (Scopus)

Abstract

This paper studies the existence, asymptotic decay rates, nonlinear stability, wave speed and chemical diffusion limits of traveling wave solutions to a chemotaxis model describing the initiation of angiogenesis and reinforced random walk. By transforming the chemotaxis system, via a Hopf-Cole transformation, into a system of conservation laws, the authors studied the traveling wave solutions of the transformed system in previous papers. One of the purposes of this paper is to transfer the results of the transformed system to the original Keller-Segel chemotaxis model. It turns out that only partial results of the transformed system have physical meaning when they are passed back to the original system. Thus the transformed system is not entirely equivalent to the original system. Particularly the chemical growth rate parameter appeared in the original system vanishes in the transformed system. Hence to understand the role of this parameter, one has to go back to the original system. Moreover, we establish some new results on zero chemical diffusion limits of traveling wave solutions. Numerical simulations of steadily propagating waves are shown.
Original languageEnglish
Pages (from-to)161-168
Number of pages8
JournalMathematical Biosciences
Volume240
Issue number2
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • Asymptotic behavior
  • Chemotaxis
  • Conservation laws
  • Nonlinear stability
  • Traveling waves
  • Wave speed

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Modelling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Cite this