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Communications in Mathematical Sciences
Volume 20 (2022)
Number 2
The Bramson correction for integro-differential Fisher–KPP equations
Pages: 563 – 596
DOI: https://dx.doi.org/10.4310/CMS.2022.v20.n2.a12
Author
Abstract
We consider integro-differential Fisher–KPP equations with nonlocal diffusion. For typical equations, we establish the logarithmic Bramson delay for solutions with step-like initial data. That is, these solutions resemble a front at position $c_\ast t - \frac{3}{2\lambda_\ast} \operatorname{log} t + \mathcal{O}(1)$ for explicit constants $c_\ast$ and $\lambda_\ast$. Certain strongly asymmetric diffusions exhibit more exotic behaviour.
Keywords
reaction-diffusion, integro-differential equation, Fisher–KPP, asymptotics
2010 Mathematics Subject Classification
35B40, 35K57, 60J80
Received 10 May 2020
Received revised 23 August 2021
Accepted 24 August 2021
Published 28 January 2022