# American Institute of Mathematical Sciences

May  2001, 1(2): 193-208. doi: 10.3934/dcdsb.2001.1.193

## Existence of travelling wave solutions in a combustion-radiation model

 1 Department of Mathematical Analysis, Free University, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands 2 Université Bordeaux I, Mathématiques Appliquées de Bordeaux, 33405 Talence Cedex, France 3 CEA-CESTA, BP 2, 33114 Le Barp Cedex, France

Received  November 2000 Revised  January 2001 Published  February 2001

We consider a simple model of premixed flames propagating in a gaseous mixture containing inert dust. The radiation field is modelled by the classical Eddington equation. The main parameters are the dimensionless opacity and the Boltzmann number. We prove the existence of travelling solutions with increased speed w.r.t. the adiabatic case. Several singular limiting cases (including a modification involving an ignition temperature) of the parameter values are discussed.
Citation: Claude-Michael Brauner, Josephus Hulshof, J.-F. Ripoll. Existence of travelling wave solutions in a combustion-radiation model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 193-208. doi: 10.3934/dcdsb.2001.1.193
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