Advances in Differential Equations

Asymptotic analysis of a parabolic system arising in combustion theory

Anne Langlois and Martine Marion

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We consider a one-dimensional parabolic system which describes the propagation of a flame with Lewis number close to one. We first prove estimates on the solutions that are independent of the activation energy. Next, we investigate the high activation energy asymptotics and derive the limiting free boundary problem. Our results rigorously justify the models currently used by physicists.

Article information

Adv. Differential Equations, Volume 14, Number 1/2 (2009), 55-86.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57: Reaction-diffusion equations 35R35: Free boundary problems 80A25: Combustion 35B25: Singular perturbations


Langlois, Anne; Marion, Martine. Asymptotic analysis of a parabolic system arising in combustion theory. Adv. Differential Equations 14 (2009), no. 1/2, 55--86.

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