A mathematical model for the filtration gas combustion taking into account thermal conductivity, diffusion, and intense interfacial heat transfer is presented. The temperature dependence of the chemical reaction rate is approximated by a δ-function and the thermal-expansion coefficient of gases behind the combustion front is taken into account. Unsteady combustion regimes are analyzed using the method of small perturbations. The boundaries of the longitudinal and spatial stability for steady regimes of the filtration combustion wave are obtained. The dependence of the Lewis number on the thermal-expansion coefficient of the gas mixture along the boundary of stability is derived, along with other relations.
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