Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth

Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth

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.

Author Details

P. M. Tchepmo Djomegni

K. S. Govinder