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

. 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 a...

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Bibliographic Details
Published in:The European physical journal. B, Condensed matter physics Condensed matter physics, 2008-02, Vol.61 (3), p.331-334
Main Authors: Benguria, R. D., Depassier, M. C., Loss, M.
Format: Article
Language:English
Subjects:
Complex Systems
Condensed Matter Physics
Exact sciences and technology
Fluid- and Aerodynamics
Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems
Physics
Physics and Astronomy
Solid State Physics
Statistical and Nonlinear Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
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Summary:. 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.
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2008-00069-1