The Bramson correction for Fisher--KPP equations with nonlocal diffusion

2020/05/09 by Cole Graham, Graham, Cole
Mathematics · Medicine · Physics and Astronomy · #35B40 #35K57 #60J80 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2005.04524

openalex publication_date 2020/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the logarithmic Bramson correction to the position of solutions to the Fisher--KPP equation with nonlocal diffusion. Solutions with step-like initial data typically resemble a front at position c_* t - \frac32 λ_* log t + O(1) for explicit constants c_* and λ_*. However, certain singular diffusions exhibit more exotic behavior.

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