Existence of travelling wave solutions in a combustion-radiation model

Claude-Michael Brauner; Josephus Hulshof; J.-F. Ripoll

doi:10.3934/dcdsb.2001.1.193

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2001, Volume 1, Issue 2: 193-208. Doi: 10.3934/dcdsb.2001.1.193

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Existence of travelling wave solutions in a combustion-radiation model

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

Received: October 31, 2000

Revised: December 31, 2000

Published: April 2001

Abstract Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 35K55, 35B25, 80A25.

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