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

Source: [The Burgers-FKPP advection-reaction-diffusion equation with cut-off](<https://www.sota2.com/research/paper/68fa5c6c1e209131ce9d0ae1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-05-26T05:00:05.667Z

Authors: Nikola Popovic, Mariya Ptashnyk, Zak Sattar

Published: 2024-10-11T12:23:11.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2410.08763>)

[PDF](<https://arxiv.org/pdf/2410.08763.pdf>)