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arXiv · 0704.1164

Pulsating Front Speed-up and Quenching of Reaction by Fast Advection

Andrej Zlatos
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Abstract

We consider reaction-diffusion equations with combustion-type non-linearities in two dimensions and study speed-up of their pulsating fronts by general periodic incompressible flows with a cellular structure. We show that the occurence of front speed-up in the sense $\lim_{A\to\infty} c_*(A)=\infty$, with $A$ the amplitude of the flow and $c_*(A)$ the (minimal) front speed, only depends on the geometry of the flow and not on the reaction function. In particular, front speed-up happens for KPP reactions if and only if it does for ignition reactions. We also show that the flows which achieve this speed-up are precisely those which, when scaled properly, are able to quench any ignition reaction.

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Andrej Zlatos. 2007-11-05. Pulsating Front Speed-up and Quenching of Reaction by Fast Advection. https://doi.org/10.1088/0951-7715%2F20%2F12%2F009

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