Year: 2017
Author: P. M. Tchepmo Djomegni, K. S. Govinder
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 : pp. 1250–1270
Abstract
Mass migration of cells (via wave motion) plays an important role in many biological processes, particularly chemotaxis. We study the existence of travelling wave solutions for a chemotaxis model on a microscopic scale. The interaction between nutrients and chemoattractants are considered. Unlike previous approaches, we allow for diffusion of substrates, degradation of chemoattractants and cell growth (constant and linear growth rate). We apply asymptotic methods to investigate the behaviour of the solutions when cells are highly sensitive to extracellular signalling. Explicit solutions are demonstrated, and their biological implications are presented. The results presented here extend and generalize known results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0114
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 : pp. 1250–1270
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Lie symmetries velocity-jump process travelling waves asymptotic methods.