Volume 9, Issue 5
Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth

P. M. Tchepmo Djomegni & K. S. Govinder

Adv. Appl. Math. Mech., 9 (2017), pp. 1250-1270.

Published online: 2018-05

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  • 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.

  • Keywords

Lie symmetries, velocity-jump process, travelling waves, asymptotic methods.

  • AMS Subject Headings

34D20, 37N25, 92B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1250, author = {}, title = {Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0114}, url = {http://global-sci.org/intro/article_detail/aamm/12199.html} }
TY - JOUR T1 - Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1250 EP - 1270 PY - 2018 DA - 2018/05 SN - 9 DO - http://dor.org/10.4208/aamm.OA-2016-0114 UR - https://global-sci.org/intro/aamm/12199.html KW - Lie symmetries, velocity-jump process, travelling waves, asymptotic methods. AB -

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.

P. M. Tchepmo Djomegni & K. S. Govinder. (2020). Asymptotic Analysis of Travelling Wave Solutions in Chemotaxis with Growth. Advances in Applied Mathematics and Mechanics. 9 (5). 1250-1270. doi:10.4208/aamm.OA-2016-0114
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