Differential and Integral Equations
- Differential Integral Equations
- Volume 23, Number 5/6 (2010), 445-450.
On front speeds in the vanishing diffusion limit for reaction-convection-diffusion equations
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.
Differential Integral Equations, Volume 23, Number 5/6 (2010), 445-450.
First available in Project Euclid: 20 December 2012
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Gilding, Brian H. On front speeds in the vanishing diffusion limit for reaction-convection-diffusion equations. Differential Integral Equations 23 (2010), no. 5/6, 445--450. https://projecteuclid.org/euclid.die/1356019305