KPP pulsating front speed-up by flows

We obtain a criterion for pulsating front speed-up by general periodic incompressible flows in two dimensions and in the presence of KPP nonlinearities. We achieve this by showing that the ratio of the minimal front speed and the effective diffusivity of the flow is bounded away from zero and infinity by constants independent of the flow. We also study speed-up of reaction-diffusion fronts by various examples of flows in two and three dimensions.

Keywords

reaction-diffusion equations, traveling fronts, front speed-up

2010 Mathematics Subject Classification

35K57

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Published 1 January 2007