ON SINGULARITIES OF THE 2-dim GASEOUS FLAME FRONTS SIMULATED BY THE SEMILINEAR HYPERBOLIC AND PARABOLIC EQUATIONS

Report provides the experimental evidences for existence of two topologically distinct types of slow combustion waves in hydrogen-air mixtures - continuous and discontinuous. For two-dimensional propagation of the deflagration flames the characteristic singularities on the continuous reaction fronts are the cusps. Their evolution is described by the Kuramoto-Sivashinsky integro-differential equation in the hydrodynamic approximation. For singular points discovered in our experiments, focused on the propagation of systems of drifting flame balls, the following issues of their mathematical classification and modeling are discussed. What is the nature of the detected singularities and what class of the known singularities can they be attributed to? Is it possible to mathematically describe singularity dynamics using just one evolutionary equation, allowing for discontinuous solutions of the reaction front in the diffusion-thermal approximation?