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Exact solution and precise asymptotics of a Fisher–KPP type front

Abstract : The present work concerns a version of the Fisher-KPP equation where the nonlinear term is replaced by a saturation mechanism, yielding a free boundary problem with mixed conditions. Following an idea proposed in [BrunetDerrida.2015], we show that the Laplace transform of the initial condition is directly related to some functional of the front position $\mu_t$. We then obtain precise asymptotics of the front position by means of singularity analysis. In particular, we recover the so-called Ebert and van Saarloos correction [EbertvanSaarloos.2000], we obtain an additional term of order $\log t /t$ in this expansion, and we give precise conditions on the initial condition for those terms to be present.
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Contributor : Bernard Derrida <>
Submitted on : Monday, March 5, 2018 - 6:38:29 PM
Last modification on : Friday, April 10, 2020 - 5:14:30 PM

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Julien Berestycki, Éric Brunet, Bernard Derrida. Exact solution and precise asymptotics of a Fisher–KPP type front. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2018, 51 (3), ⟨10.1088/1751-8121/aa899f⟩. ⟨hal-01723857⟩



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