## Differential and Integral Equations

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

Brian H. Gilding

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 5/6 (2010), 445-450.

Dates
First available in Project Euclid: 20 December 2012