On front speeds in the vanishing diffusion limit for reaction-convection-diffusion equations

Abstract

Reaction-convection-diffusion equations with a monostable reaction term, that generalize the KPP equation, admit a global travelling-wave solution whose limiting values are the stable and unstable steady states if and only if the wave-speed is greater than or equal to some critical number. In a recent paper, Crooks and Mascia showed that, in the vanishing viscosity limit, this minimal speed tends to the corresponding minimal wave-speed associated with the first-order equation without the diffusion term. An alternative proof of this result is presented using an integral equation approach developed by the author and Robert Kersner.