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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2018

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

Résumé

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.

Dates et versions

hal-01723857 , version 1 (05-03-2018)

Identifiants

Citer

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