(1) Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile;(2) School of Mathematics, Georgia Tech, Atlanta, GA 30332, USA
Abstract:
We establish rigorous upper and lower bounds for the speed of pulled fronts with a cut-off. For all reaction terms of KPP
type a simple analytic upper bound is given. The lower bounds however depend on details of the reaction term. For a small
cut-off parameter the two leading order terms in the asymptotic expansion of the upper and lower bounds coincide and correspond
to the Brunet-Derrida formula. For large cut-off parameters the bounds do not coincide and permit a simple estimation of the
speed of the front.