Forward combustion fronts as traveling waves through a porous medium

Traveling wave combustion for a two-phase flow model that represents combustion of oil with oxygen or air in a porous medium was discussed in [1]. The discussion was limited to the case where the speed of the particles ahead of the combustion front is less than the fractional oil heat capacity. In this work we discuss the other case where the speed of the particles ahead of the combustion front is greater than the fractional oil heat capacity. Traveling waves combustion are represented by connecting orbits of a system of three ordi- nary differential equations that approach the nonhyperbolic equilibrium along its stable manifold and not along its center direction. For each set of physical parameters, we prove the existence of two distinct combustion front, with different combustion temperatures and speeds, unlike the case discussed in [1], where there is only one. The proofs use geometric singular perturbation theory.