Mathematics of traveling waves in chemotaxis - Review paper

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73 Citations (Scopus)

Abstract

This article surveys the mathematical aspects of traveling waves of a class of chemotaxis models with logarithmic sensitivity, which describe a variety of biological or medical phenomena including bacterial chemotactic motion, initiation of angiogenesis and reinforced random walks. The survey is focused on the existence, wave speed, asymptotic decay rates, stability and chemical diffusion limits of traveling wave solutions. The main approaches are reviewed and related analytical results are given with sketchy proofs. We also develop some new results with detailed proofs to fill the gap existing in the literature. The numerical simulations of steadily propagating waves will be presented along the study. Open problems are proposed for interested readers to pursue.
Original languageEnglish
Pages (from-to)601-641
Number of pages41
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume18
Issue number3
DOIs
Publication statusPublished - 1 May 2013

Keywords

  • Angiogenesis
  • Bacteria
  • Chemical diffusion
  • Chemotaxis
  • Conservation laws
  • Fisher equation
  • Stability
  • Transformation
  • Traveling waves
  • Wave speed

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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