Reaction, diffusion and chemotaxis in wave propagation

Shangbing Ai, Wenzhang Huang, Zhian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)

Abstract

By constructing an invariant set in the three dimensional space, we establish the existence of traveling wave solutions to a reaction-diffusion- chemotaxis model describing biological processes such as the bacterial chemo- tactic movement in response to oxygen and the initiation of angiogenesis. The minimal wave speed is shown to exist and the role of each process of reaction, diffusion and chemotaxis in the wave propagation is investigated. Our results reveal three essential biological implications: (1) the cell growth increases the wave speed; (2) the chemotaxis must be strong enough to make a contribu- tion to the increment of the wave speed; (3) the diffusion rate plays a role in increasing the wave speed only when the cell growth is present.
Original languageEnglish
Pages (from-to)1-21
Number of pages21
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume20
Issue number1
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Cell growth
  • Minimal wave speed
  • Reaction-diffusion-chemotaxis
  • Traveling waves

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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