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Journal Articles Journal of the European Mathematical Society Year : 2019

Chemotactic waves of bacteria at the mesoscale

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. Counterexamples to both existence and uniqueness are found numerically after careful analysis of the discrete velocity problem.
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hal-01340375 , version 1 (01-07-2016)

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Vincent Calvez. Chemotactic waves of bacteria at the mesoscale. Journal of the European Mathematical Society, 2019, 22 (2), pp.593-668. ⟨10.4171/JEMS/929⟩. ⟨hal-01340375⟩
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