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Chemotactic waves of bacteria at the mesoscale

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.

preprint2016arXivOpen access
Vincent Calvez
math.APcond-mat.soft
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Vincent Calvez

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