A threshold phenomenon in the propagation of a point source initiated flame

This work concerns an asymptotic model for spherical flame propagation, derived by Joulin [Comb. Sci. Tech. 43 (1985) 99-113]. In Joulin's paper, the flame radius is governed by a singular integro-differential equation, and its long-time behaviour is seen numerically to depend on an energy input parameter. Three regimes are identified: the flame radius may either shrink to 0, or tend to +∞, or tend to a finite value. The purpose of the present work is to give a mathematically rigorous proof of these results.