  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.
