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July  2008, 10(1): 73-90. doi: 10.3934/dcdsb.2008.10.73

Travelling waves for a combustion model coupled with hyperbolic radiation moment models

Josephus Hulshof 1, and  Pascal Noble 2,

1. 

Faculty of Sciences – Mathematics and Computer Science division, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081HV Amsterdam
2. 

Université Claude Bernard, Institut Camille Jordan, 43, boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

Received  December 2006 Revised  March 2008 Published  April 2008

In this paper we consider a model of a flame propagating in a gas containing inert dust. The combustion model is a model with simple chemistry obtained in the high activation energy limit. The radiative field is modeled either by the $P_1$ isotropic model or by the $M_1$ anisotropic model. Under some restrictions on the parameters we prove the existence of travelling waves for this hierarchy of combustion radiation models by Schauder's fixed point argument on bounded domains and uniform estimates.
Keywords: radiation, combustion, pre-mixed flames, Travelling waves, momentum models..
Mathematics Subject Classification: Primary: 35R35; 35M10; Secondary: 80A2.
Citation: Josephus Hulshof, Pascal Noble. Travelling waves for a combustion model coupled with hyperbolic radiation moment models. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 73-90. doi: 10.3934/dcdsb.2008.10.73
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