NDLI: Travelling Chemotactic Aggregates at Mesoscopic Scale and BiStability

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Calvez, Vincent Twarogowska, Monika Gosse, Laurent
Copyright Year	2017
Abstract	A model consisting of a kinetic equation for run-and-tumble biased bacteria motion, coupled with two reaction-diffusion equations for chemical signals, is studied. It displays time-asymptotic propagation at constant velocity, i.e., aggregated travelling (exponential) layers. To capture them for various parameters, a well-balanced setup is based on both Case's elementary solutions" and $\mathcal{L}$-spline reconstruction. Far from the diffusive regime, waves travelling at different velocities (bistability) are proved to coexist. Numerics suggest that they are locally asymptotically stable, so that the resulting bifurcation diagram shows counterintuitive features.
Sponsorship	H2020 European Research Council
Starting Page	2224
Ending Page	2249
Page Count	26
File Format	PDF
ISSN	00361399
DOI	10.1137/16M1108108
e-ISSN	1095712X
Issue Number	6
Volume Number	77
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2017-12-14
Access Restriction	Subscribed
Subject Keyword	solitary wave Kinetics in biochemical problems PDEs in connection with biology and other natural sciences kinetic model exponential layers Cell biology run-and-tumble chemotaxis Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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