A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.
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Jean-Michel Roquejoffre, Peter Constantin, Lenya Ryzhik, Komla Domelevo, Existence of pulsating waves in a model of flames in sprays. J. Eur. Math. Soc. 8 (2006), no. 4, pp. 555–584DOI 10.4171/JEMS/67