Journal of the European Mathematical Society


Full-Text PDF (224 KB) | Metadata | Table of Contents | JEMS summary
Volume 8, Issue 4, 2006, pp. 555–584
DOI: 10.4171/JEMS/67

Existence of pulsating waves in a model of flames in sprays

Peter Constantin[1], Komla Domelevo[2], Jean-Michel Roquejoffre[3] and Lenya Ryzhik[4]

(1) Department of Mathematics, Princeton University, Fine Hall, Washington Road, NJ 08544-1000, PRINCETON, UNITED STATES
(2) UFR-MIG, UMR CNRS 5640, Université Paul Sabatier, 118 route de Narbonne, F-31062, TOULOUSE CEDEX, FRANCE
(3) Institut de Mathématiques (UMR CNRS 5219), Université Paul Sabatier, 118 route de Narbonne, 31062, TOULOUSE CEDEX, FRANCE
(4) Department of Mathematics, Stanford University, CA 94305, STANFORD, UNITED STATES

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.

Keywords: Inverse mean curvature flow, weak solution, level set formulation, p-harmonic function

Constantin Peter, Domelevo Komla, Roquejoffre Jean-Michel, Ryzhik Lenya: Existence of pulsating waves in a model of flames in sprays. J. Eur. Math. Soc. 8 (2006), 555-584. doi: 10.4171/JEMS/67