Localization of Singular Integral Operators.
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.
In this paper, we formulate necessary conditions for decay rates of Lp operator norms of weighted oscillatory integral operators R and give sharp L2 estimates and nearly sharp Lp estimates.