English

Concentration waves of chemotactic bacteria: the discrete velocity case

Analysis of PDEs 2018-11-20 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1811.07563,
  title  = {Concentration waves of chemotactic bacteria: the discrete velocity case},
  author = {Vincent Calvez and Laurent Gosse and Monika Twarogowska},
  journal= {arXiv preprint arXiv:1811.07563},
  year   = {2018}
}