We study a model for the injection of air into an underground porous medium that contains a solid fuel. In our previous works the model was simplified and all wave sequences for the Riemann problem solution were obtained without taking into account thermal losses to the surrounding rock. In this work the first step is made to understand the effect of heat losses, which are important especially in laboratory experiments. In order to simplify the proof of the existence and uniqueness of the traveling wave solution, we disregard diffusion effects and the dependence of gas density on temperature.
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