Preprint 62/2016

Wavenumber selection in coupled transport equations

Arnd Scheel and Angela Stevens

Contact the author: Please use for correspondence this email.
Submission date: 20. Sep. 2016
Pages: 25
published in: Journal of mathematical biology, 75 (2017) 5, p. 1047-1073 
DOI number (of the published article): 10.1007/s00285-017-1107-8
Bibtex
Keywords and phrases: traveling wave, standing wave, balance laws, coupled transport equations, invasion fronts, wavenumber selection
Download full preprint: PDF (7149 kB)

Abstract:
We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle selection mechanism for the wavenumbers of spatio-temporally periodic waves. We comment on possible implications for rippling patterns observed in colonies of myxobacteria.

18.10.2019, 02:16