Chemotactic waves of bacteria at the mesoscale
Analysis of PDEs
2016-07-05 v1 Soft Condensed Matter
Abstract
The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two reaction-diffusion equations for the chemical signals. Strong mathematical difficulties arise in comparison with the diffusive regime which was studied in a previous work. The cornerstone of the proof consists in establishing monotonicity properties of the spatial density of cells. Travelling waves exist under certain conditions on the parameters. Counter-examples to both existence and uniqueness are found numerically after careful analysis of the discrete velocity problem.
Keywords
Cite
@article{arxiv.1607.00429,
title = {Chemotactic waves of bacteria at the mesoscale},
author = {Vincent Calvez},
journal= {arXiv preprint arXiv:1607.00429},
year = {2016}
}
Comments
72 pages, 15 figures