An asymptotic fractional differential model of spherical flame

Free access article

Issue		ESAIM: Proc. Volume 5, 1998 Fractional Differential Systems: Models, Methods and Applications


Page(s)		15 - 27
DOI		http://dx.doi.org/10.1051/proc:1998009

ESAIM: Proc., 1998, Vol. 5, pp. 15-27
DOI: 10.1051/proc:1998009

An asymptotic fractional differential model of spherical flame

Jacques Audounet and Jean-Michel Roquejoffre

UFR MIG, UMR C.N.R.S. 5640, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex, France

Abstract
This paper is devoted to the analysis and numerical simulation of a model of initiation of a small spherical flame by a point source derived by G. Joulin. This asymptotical model for large activation energies gives the radius of the flame 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 diffusive representation.

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