American Institute of Mathematical Sciences

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

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

Jean-Michel Roquejoffre 1, and  Juan-Luis Vázquez 2,

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.
Keywords: integro-differential equation, Flame ball, blow-up., critical energy.
Mathematics Subject Classification: 35B3.
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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