On the speed of pulled fronts with a cutoff

Abstract

We study the effect of a small cutoff $\epsilon$ on the velocity of a pulled front in one dimension by means of a variational principle. We obtain a lower bound on the speed dependent on the cutoff, and for which the two leading order terms correspond to the Brunet Derrida expression. To do so we cast a known variational principle for the speed of propagation of fronts in new variables which makes it more suitable for applications.

12 pages no figures

References in corpus (1)

• A phenomenological theory giving the full statistics of the position of fluctuating pulled fronts

Cited by in corpus (7)

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• Shift in the speed of reaction diffusion equation with a cut-off: pushed and bistable fronts
• The Evolution of Travelling Waves in a KPP Reaction-Diffusion Model with Cut-off Reaction Rate. I. Permanent Form Travelling Waves
• Equivalence of variational principles to determine the speed of scalar reaction diffusion fronts
• Rigorous results for the speed of Kolmogorov--Petrovskii--Piscounov fronts with a cutoff