Singularity of a combustion wave profile: a clue to the multicomponent theory for liquid-gas filtration combustion

Abstract

We study a nonlinear wave for a system of balance laws in one space dimension, which describes combustion for two-phase (gas and liquid) flow in porous medium. The problem is formulated for a general $N$-component liquid for modeling the strong multicomponent effects reported recently for an application to light oil recovery by air injection. Despite the immense complexity of the model, the problem allows analytic solution. The clue to this solution is a special form of a folding singularity, which occurs at an internal point of the wave profile. Analysis of this singularity provides a missing determining relation for wave parameters. This result is not only interesting for the application under consideration, but also motivates a deeper mathematical study of such singularities for general systems of balance laws.