A threshold phenomenon in the propagation of a point source initiated flame

Jacques Audounet; Vincent Giovangigli; Jean Michel Roquejoffre

doi:10.1016/S0167-2789(98)00153-5

A threshold phenomenon in the propagation of a point source initiated flame

Jacques Audounet
, Vincent Giovangigli
, Jean Michel Roquejoffre

Université de Toulouse

Research output: Contribution to journal › Article › peer-review

Abstract

This work concerns an asymptotic model for spherical flame propagation, derived by Joulin [Comb. Sci. Tech. 43 (1985) 99-113]. In Joulin's paper, the flame radius is governed by a singular integro-differential equation, and its long-time behaviour is seen numerically to depend on an energy input parameter. Three regimes are identified: the flame radius may either shrink to 0, or tend to +∞, or tend to a finite value. The purpose of the present work is to give a mathematically rigorous proof of these results.

Original language	English
Pages (from-to)	295-316
Number of pages	22
Journal	Physica D: Nonlinear Phenomena
Volume	121
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(98)00153-5
Publication status	Published - 1 Jan 1998

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abstract = "This work concerns an asymptotic model for spherical flame propagation, derived by Joulin [Comb. Sci. Tech. 43 (1985) 99-113]. In Joulin's paper, the flame radius is governed by a singular integro-differential equation, and its long-time behaviour is seen numerically to depend on an energy input parameter. Three regimes are identified: the flame radius may either shrink to 0, or tend to +∞, or tend to a finite value. The purpose of the present work is to give a mathematically rigorous proof of these results.",

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AB - This work concerns an asymptotic model for spherical flame propagation, derived by Joulin [Comb. Sci. Tech. 43 (1985) 99-113]. In Joulin's paper, the flame radius is governed by a singular integro-differential equation, and its long-time behaviour is seen numerically to depend on an energy input parameter. Three regimes are identified: the flame radius may either shrink to 0, or tend to +∞, or tend to a finite value. The purpose of the present work is to give a mathematically rigorous proof of these results.

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A threshold phenomenon in the propagation of a point source initiated flame

Abstract

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