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 co-existence of several travelling waves for some sets of parameters, as well as the possible non-existence of travelling waves.
CITATION STYLE
Calvez, V., Gosse, L., & Twarogowska, M. (2017). Concentration waves of chemotactic bacteria: The discrete velocity case. Springer INdAM Series, 16, 79–109. https://doi.org/10.1007/978-3-319-49262-9_3
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