Rigorous results for the minimal speed of Kolmogorov–Petrovskii–Piscounov monotonic fronts with a cutoff

Rafael D. Benguria, M. Cristina Depassier, Michael Loss
2012 Journal of Mathematical Physics  
We study the effect of a cutoff on the speed of pulled fronts of the one-dimensional reaction diffusion equation. To accomplish this, we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles. This existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of
more » ... he cut-off parameter ε. From these bounds we estimate the range of validity of the Brunet-Derrida formula for a general class of reaction terms. C 2012 American Institute of Physics. [http://dx.
doi:10.1063/1.4770248 fatcat:koyxmpo7c5fjvo5d6smccvhgci