Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames

Abstract

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. To cite this article: C. Lederman et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 569–574.