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.
From: Zakee Sattar [view email]
[v1]
Fri, 11 Oct 2024 12:23:11 UTC (629 KB)
[v2]
Fri, 22 May 2026 09:47:42 UTC (647 KB)
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