Advances in Differential Equations

Asymptotic analysis of a parabolic system arising in combustion theory

Anne Langlois and Martine Marion

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Abstract

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

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867278

Mathematical Reviews number (MathSciNet)
MR2478929

Zentralblatt MATH identifier
1207.35033

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

Citation

Langlois, Anne; Marion, Martine. Asymptotic analysis of a parabolic system arising in combustion theory. Adv. Differential Equations 14 (2009), no. 1/2, 55--86. https://projecteuclid.org/euclid.ade/1355867278.


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