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

Abstract

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.