Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/35826
Title: Reaction, diffusion and chemotaxis in wave propagation
Authors: Ai, SB
Huang, WZ
Wang, ZA 
Keywords: Reaction-diffusion-chemotaxis
Cell growth
Traveling waves
Minimal wave speed
Issue Date: 2015
Publisher: American Institute of Mathematical Sciences
Source: Discrete and continuous dynamical systems. Series B, 2015, v. 20, no. 1, p. 1-21 How to cite?
Journal: Discrete and continuous dynamical systems. Series B 
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 chemotactic 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 contribution 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.
URI: http://hdl.handle.net/10397/35826
ISSN: 1531-3492 (print)
1553-524X (online)
DOI: 10.3934/dcdsb.2015.20.1
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