Upper and lower bounds for the speed of pulled fronts with a cut-off
Facultad de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
2 School of Mathematics, Georgia Tech, Atlanta, GA, 30332, USA
Corresponding author: a email@example.com
Published online: 20 February 2008
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.
PACS: 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008