# American Institute of Mathematical Sciences

August  2002, 2(3): 379-387. doi: 10.3934/dcdsb.2002.2.379

## Ignition and propagation in an integro-differential model for spherical flames

 1 Laboratoire MIP, Université Paul Sabatier, 31062 Toulouse Cedex 9, France 2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28046 Madrid, Spain

Received  September 2001 Revised  December 2001 Published  May 2002

A uniform lower bound for the energy involved in the propagation of a flame is given. Such a bound is important for safety considerations. In the integro-differential model the spherical flame originates from a point source which supplies a finite amount of energy over time. It is proved here that, independently of the form of the heat source function, a minimal energy is required for the propagation of the flame. The effect of a spark is then studied.
Citation: Jean-Michel Roquejoffre, Juan-Luis Vázquez. Ignition and propagation in an integro-differential model for spherical flames. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 379-387. doi: 10.3934/dcdsb.2002.2.379
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