ABSTRACT
This article is devoted to the study of a flame ball model, derived by G. Joulin, which satisfies a singular integro-differential equation. We prove that, when radiative heat losses are too important, the flame always quenches; when heat losses are smaller, it stabilizes or quenches, depending on an energy input parameter. We also examine the asymptotics of the radius for these different regimes.
Key words: flame ball, integro-differential equation, parabolic problem, asymptotic
behavior.
2000 Mathematics Subject Classification: 35B30, 35B40, 35K05, 45J05.