Steady states of the surface of a nonadiabatic flame near the limits

Within the framework of a weakly linear model, which describes a nonadiabatic flame near the limit of its propagation caused by heat losses, steady states of the combustion-wave from are studied. Three-dimensional structures of the wave front are formed because of diffusion-thermal instability of the planar flame. The limits of propagation of a curved flame front are shown to expand if the diffusion-thermal instability is taken into account: a cellular flame can exist at heat losses higher than the critical value for the two-dimensional flame. The stability of steady solutions, which describe the cellular flame near the limits of its propagation, is studied. For sufficiently high heat losses, steady solutions for a nonadiabatic flame with front discontinities are obtained.