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

被引：1

作者：

Boutillon, Nathanael ^{[1
,2
]}

机构：

[1] INRAE, BioSP, F-84914 Avignon, France

[2] Aix Marseille Univ, CNRS, I2M, Marseille, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 240卷

关键词：

Fisher-KPP equations; Nonlocal diffusion equations; Logarithmic correction; Probabilistic representation; Large deviations; BRAMSON CORRECTION; CONVERGENCE; KOLMOGOROV; DISPERSAL; PROPAGATION; POPULATION;

D O I：

10.1016/j.na.2023.113465

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 thin-tailed kernels.

引用

页数：12

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