Propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion

Abstract

The propagation of fronts in the Fisher-Kolmogorov equation with spatially varying diffusion coefficients is studied. Using coordinate changes, WKB approximations, and multiple scales analysis, we provide an analytic framework that describes propagation of the front up to the minimum of the diffusion coefficient. We also present results showing the behavior of the front after it passes the minimum. In each case, we show that standard traveling coordinate frames do not properly describe front propagation. Lastly, we provide numerical simulations to support our analysis and to show, that around the minimum, the motion of the front is arrested on asymptotically significant timescales.