Full paper in PDF:
$%H. Rouzaud, Long-time dynamics of an integro-differential equation describing the evolution of a spherical flame, Rev. Mat. Complut. 16 (2003), no. 1, 207232.%$
Long-Time Dynamics of an Integro-Differential Equation Describing the Evolution of a Spherical Flame
Hélène ROUZAUD
Laboratoire M.I.P., U.M.R. 5640
Université Paul Sabatier Toulouse III
118 route de Narbonn
31062 Toulouse Cedex 4 — France

Received: October 15, 2001
Accepted: April 29. 2002

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.