Abstract
The phenomenon of pressure driven flames in inert porous media filled with a flammable gaseous mixture is considered in the present work. We focus on the travelling wave solutions arising in the adiabatic model of this phenomenon that was developed and studied in [2, 3, 5, 6]. We start with the simplest possible model which describes the combustion process in inert porous media in the absence of inertial effects, hydraulic resistance, and thermo conductivity. For this model, the existence and uniqueness of the subsonic reaction wave were proved under reasonable assumptions. This simplest model is characterized by the linear dependence of friction force on the velocity of gaseous mixture.
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