Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff

Abstract

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cutoff. We show that the Brunet-Derrida formula corresponds to the leading order expansion in the cut-off parameter of both the upper and lower bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula lies outside the allowed band determined from the bounds. If nonlinearities are neglected the upper and lower bounds coincide and are the exact linear speed for all values of the cut-off parameter.

8 pages, 3 figures

References in corpus (3)

• Geometric scaling as traveling waves
• Effects of Fluctuations on Propagating Fronts
• On the speed of pulled fronts with a cutoff

Cited by in corpus (4)

• Speed selection and stability of wavefronts for delayed monostable reaction-diffusion equations
• Cross-overs of Bramson's shift at the transition between pulled and pushed fronts
• The Evolution of Travelling Waves in a KPP Reaction-Diffusion Model with Cut-off Reaction Rate. I. Permanent Form Travelling Waves
• Rigorous results for the speed of Kolmogorov--Petrovskii--Piscounov fronts with a cutoff