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.
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Benguria, R., Depassier, M. & Loss, M. Upper and lower bounds for the speed of pulled fronts with a cut-off. Eur. Phys. J. B 61, 331–334 (2008). https://doi.org/10.1140/epjb/e2008-00069-1
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DOI: https://doi.org/10.1140/epjb/e2008-00069-1