Rigorous results for the speed of Kolmogorov--Petrovskii--Piscounov fronts with a cutoff

Details Rigorous results for the speed of Kolmogorov--Petrovskii--Piscounov fronts with a cutoff Rigorous results for the speed of Kolmogorov--Petrovskii--Piscounov fronts with a cutoff

2010-10-14

arxiv.org/abs/1010.3044v1

Physics

Mathematical Physics

LaTeX, 17 pages, 1 figure

Scientific paper

We study the effect of a cut-off on the speed of pulled fronts of the one
dimensional reaction diffusion equation. We prove rigorous upper and lower
bounds on the speed in terms of the cut-off parameter epsilon. From these
bounds we estimate the range of validity of the Brunet--Derrida formula for a
general class of reaction terms.

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