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

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  • R. D. Benguria
  • M. C. Depassier
  • M. Loss

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

Suggested Citation

  • R. D. Benguria & M. C. Depassier & M. Loss, 2008. "Upper and lower bounds for the speed of pulled fronts with a cut-off," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 61(3), pages 331-334, February.
    • Handle: RePEc:spr:eurphb:v:61:y:2008:i:3:p:331-334
    DOI: 10.1140/epjb/e2008-00069-1
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    Cited by:

    1. Bozzini, Benedetto & Lacitignola, Deborah & Sgura, Ivonne, 2011. "Travelling waves in a reaction-diffusion model for electrodeposition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1027-1044.

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