Differential and Integral Equations

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

Brian H. Gilding

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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

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

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35C07: Traveling wave solutions 35K10: Second-order parabolic equations 35A18: Wave front sets


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

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