The Burgers-FKPP advection-reaction-diffusion equation with cut-off

Abstract

We investigate the effect of a Heaviside cut-off on the front propagation dynamics of the so-called Burgers-FisherKolmogoroff-Petrowskii-Piscounov (Burgers-FKPP) advection-reaction-diffusion equation. We prove the existence and uniqueness of a travelling front solution in the presence of a cut-off in the reaction kinetics and the advection term, and we derive the leading-order asymptotics for the speed of propagation of the front in dependence on the advection strength and the cut-off parameter. Our analysis relies on geometric techniques from dynamical systems theory and specifically, on geometric desingularisation, which also known as blow-up.