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

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

29 pages