Concentration waves of chemotactic bacteria: the discrete velocity case

Vincent Calvez (1) , Laurent Gosse (2) , Monika Twarogowska (3)

1 MMCS - Modélisation mathématique, calcul scientifique
2 IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone"
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The existence of travelling waves for a coupled system of hyperbolic/ parabolic equations is established in the case of a finite number of velocities in the kinetic equation. This finds application in collective motion of chemotactic bacteria. The analysis builds on the previous work by the first author (arXiv:1607.00429) in the case of a continuum of velocities. Here, the proof is specific to the discrete setting, based on the decomposition of the population density in special Case's modes. Some counter-intuitive results are discussed numerically, including the coexistence of several travelling waves for some sets of parameters, as well as the possible non-existence of travelling waves.

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Calvez, Laurent Gosse, Monika Twarogowska. Concentration waves of chemotactic bacteria: the discrete velocity case. Innovative Algorithms and Analysis, Springer International Publishing, 2017. ⟨hal-01924071⟩