[Justification mathématique d'une équation intégro-différentielle non linéaire pour un modèle de flamme sphérique]
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.
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.
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@article{CRMATH_2002__334_7_569_0,
author = {Lederman, Claudia and Roquejoffre, Jean-Michel and Wolanski, Noemi},
title = {Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames},
journal = {Comptes Rendus. Math\'ematique},
pages = {569--574},
publisher = {Elsevier},
volume = {334},
number = {7},
year = {2002},
doi = {10.1016/S1631-073X(02)02299-9},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02299-9/}
}
TY - JOUR AU - Lederman, Claudia AU - Roquejoffre, Jean-Michel AU - Wolanski, Noemi TI - Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames JO - Comptes Rendus. Mathématique PY - 2002 SP - 569 EP - 574 VL - 334 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02299-9/ DO - 10.1016/S1631-073X(02)02299-9 LA - en ID - CRMATH_2002__334_7_569_0 ER -
%0 Journal Article %A Lederman, Claudia %A Roquejoffre, Jean-Michel %A Wolanski, Noemi %T Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames %J Comptes Rendus. Mathématique %D 2002 %P 569-574 %V 334 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02299-9/ %R 10.1016/S1631-073X(02)02299-9 %G en %F CRMATH_2002__334_7_569_0
Lederman, Claudia; Roquejoffre, Jean-Michel; Wolanski, Noemi. Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames. Comptes Rendus. Mathématique, Tome 334 (2002) no. 7, pp. 569-574. doi : 10.1016/S1631-073X(02)02299-9. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02299-9/
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