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Title: Flow-distributed spikes for Schnakenberg kinetics
Authors: Wei, J
Winter, M
Keywords: Pattern formation;Convection;Spike;Steady-states;Stability;Left/right asymmetry;Primary 35B36;92E20;Secondary 35B35;76E06
Issue Date: 2012
Publisher: Springer-Verlag
Citation: Journal of Mathematical Biology, 64(1-2), 211 - 254, 2012
Abstract: We study a system of reaction–diffusion–convection equations which combine a reaction–diffusion system with Schnakenberg kinetics and the convective flow equations. It serves as a simple model for flow-distributed pattern formation. We show how the choice of boundary conditions and the size of the flow influence the positions of the emerging spiky patterns and give conditions when they are shifted to the right or to the left. Further, we analyze the shape and prove the stability of the spikes. This paper is the first providing a rigorous analysis of spiky patterns for reaction-diffusion systems coupled with convective flow. The importance of these results for biological applications, in particular the formation of left–right asymmetry in the mouse, is indicated.
Description: This is the post-print version of the final published paper. The final publication is available at by following the link below. Copyright @ 2011 Springer-Verlag.
ISSN: 0303-6812
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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