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

Cole Graham

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arXiv · 2005.04524

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

Cole Graham

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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 $c_{*} t - \frac{3}{2 \lambda_{*}} \log t + \mathcal{O}(1)$ for explicit constants $c_{*}$ and $\lambda_{*}$. However, certain singular diffusions exhibit more exotic behavior.

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Cole Graham. 2020-05-09. The Bramson correction for Fisher--KPP equations with nonlocal diffusion. https://arxiv.org/abs/2005.04524

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