Closed Description of Stationary Flames

The problem of non-perturbative description of stationary flames with arbitrary gas expansion is considered. A general method for deriving equations for the flame front position is developed. On the basis of the Thomson circulation theorem an implicit integral of the flow equations is constructed. With the help of this integral the flow structure near the flame front is determined, and a closed system of equations for the flame front position and a set of auxiliary quantities is obtained. This system is shown to be quasi-local, and its transverse representation is found. This representation allows reduction of the system to a single equation for the flame front position. The developed approach is applied to the case of zero-thickness flames.