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arXiv · 2410.08763

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

Nikola Popovic·Mariya Ptashnyk·Zak Sattar
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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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Nikola Popovic, Mariya Ptashnyk, Zak Sattar. 2024-10-11. The Burgers-FKPP advection-reaction-diffusion equation with cut-off. https://arxiv.org/abs/2410.08763

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