The solution is never steady-state. The combustion front is moving forward and the temperature and saturation profile is constantly changing. Steady-state assumption is just considered at the close vicinity of the combustion front to enable analytical modelling \cite{Aldushin_1981}. While simpler model \cite{Lebedev_1976} suggests the existence of oscillatory behavior in the unstable region, our model relies on the numerical observation of physical instabilities. Pulsating behavior observed in our simulation is independent of the temporal and spatial refinement. Small changes of parameters, even in the unstable region, do not cause divergence from the original simulation results (see part 4).