Article Dans Une Revue Nonlinear Analysis Année : 2024

Large deviations and the emergence of a logarithmic delay in a nonlocal Fisher-KPP equation

Résumé

We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude that the logarithmic delay emerges also for the solutions of the nonlinear equation. Previous papers found very precise results for the nonlinear equation with strong assumptions on the decay of the kernel. Our results are less precise, but they are valid for all continuous symmetric thin-tailed kernels.

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Dates et versions

hal-03637731 , version 1 (11-04-2022)
hal-03637731 , version 2 (20-05-2022)

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Nathanaël Boutillon. Large deviations and the emergence of a logarithmic delay in a nonlocal Fisher-KPP equation. Nonlinear Analysis, 2024, 240, pp.113465. ⟨10.1016/j.na.2023.113465⟩. ⟨hal-03637731v2⟩
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