  In this paper we study the stability of fronts in a reduction of a well-known
PDE system that is used to model the combustion in hydraulically resistant
porous media. More precisely, we consider the original PDE system under the
assumption that one of the parameters of the model, the Lewis number, is chosen
in a specific way and with initial conditions of a specific form. {For a class
of initial conditions, then the number of unknown functions is reduced from
three to two. For the reduced system, the existence of combustion fronts
follows from the existence results for the original system. The stability of
these fronts is studied here by a combination of energy estimates and numerical
Evans function computations and nonlinear analysis when applicable. We then
lift the restriction on the initial conditions and show that the stability
results obtained for the reduced system extend to the fronts in the full system
considered for that specific value of the Lewis number. The fronts that we
{investigate} are proved to be either absolutely unstable or convectively
unstable on the nonlinear level.
