Two-dimensional quasiharmonic dissipative structures in gas flames and their stability

Two-dimensional (2D) cellular stationary structures of combustion fronts in gases are discussed. The absence of stable stationary structures on plane or spherical surfaces is shown. In the case of a sufficiently slowly expanding cylindrical flame a quasi-one-dimensional (Q1D) structure, which is uniform along the cyclic coordinate, must be followed by a rectangular parket, and then an essentially nonstationary combustion regime is to be expected.