Comptes Rendus
Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames
Comptes Rendus. Mathématique, Volume 334 (2002) no. 7, pp. 569-574.

This Note is devoted to the justification of an asymptotic model for quasisteady three-dimensional spherical flames proposed by G. Joulin [7]. The paper [7] derives, by means of a three-scale matched asymptotic expansion, starting from the classical thermo-diffusive model with high activation energies, an integro-differential equation for the flame radius. In the derivation, it is essential for the Lewis number – i.e., the ratio between thermal and molecular diffusion – to be strictly less than unity. In this Note, we give the main ideas of a rigorous proof of the validity of this model, under the additional restriction that the Lewis number is close to 1.

Nous donnons dans cette Note les grandes lignes de la justification mathématiquement rigoureuse d'un modèle intégro-différentiel non linéaire d'évolution du rayon d'une flamme sphérique initialement proposé par G. Joulin dans [7]. Cette équation est obtenue dans le cadre du modèle thermo-diffusif tridimensionnel aux hautes énergies d'activation, avec nombre de Lewis strictement plus petit que 1. Nous montrons dans cette note la validité du modèle sous la restriction supplémentaire que le nombre de Lewis est assez proche de 1.

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Published online:
DOI: 10.1016/S1631-073X(02)02299-9
Claudia Lederman 1; Jean-Michel Roquejoffre 2; Noemi Wolanski 1

1 Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
2 UFR-MIG, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse cedex, France
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Claudia Lederman; Jean-Michel Roquejoffre; Noemi Wolanski. Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames. Comptes Rendus. Mathématique, Volume 334 (2002) no. 7, pp. 569-574. doi : 10.1016/S1631-073X(02)02299-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02299-9/

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[6] L. Glangetas; J.-M. Roquejoffre Bifurcations of travelling waves in the thermo-diffusive model for flame propagation, Arch. Rational Mech. Anal., Volume 134 (1996), pp. 341-402

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[8] G. Joulin Preferential diffusion and the initiation of lean flames of light fuels, SIAM J. Appl. Math., Volume 47 (1987), pp. 998-1016

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