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Abstract. This paper is devoted to the analysis and numerical simulation of a model of initiation of a small spherical ame by a p o i n t source derived by G. Joulin. This asymptotical model for large activation energies gives the radius of the ame as the solution of a nonlinear Abel integral equation of the second type. The analysis (existence, uniqueness, qualitative comportement and power threshold) and one step numerical simulation use both classical integral equation tools and di usive representation.