Open AccessReaction, diffusion and chemotaxis in wave propagation
Author(s) -
Shangbing Ai,
Wenzhang Huang,
ZhiAn Wang
Publication year - 2015
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2015.20.1
Subject(s) - chemotaxis , reaction–diffusion system , diffusion , wave speed , traveling wave , invariant (physics) , wave propagation , physics , mathematical analysis , mechanics , mathematics , chemistry , optics , thermodynamics , mathematical physics , biochemistry , receptor
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.Department of Applied Mathematic