Upper and lower bounds for the speed of pulled fronts with a cut-off

R. D. Benguria, M. C. Depassier () and M. Loss

The European Physical Journal B: Condensed Matter and Complex Systems, 2008, vol. 61, issue 3, 331-334

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008

Keywords: 82.40.Ck Pattern formation in reactions with diffusion; flow and heat transfer; 52.35.Mw Nonlinear phenomena: waves; wave propagation; and other interactions; 02.30.Xx Calculus of variations (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1140/epjb/e2008-00069-1

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