Asymptotics of critical conditions in one combustion model

The work is devoted to solving the problem of critical conditions for an autocatalytic combustion model, taking into account the consumption of reagent and oxidizer. By use the methods of geometric theory of singular perturbations, the analysis of the mathematical model of this process show that there are two main types of combustion modes: the slow combustion mode and the thermal explosion mode. The critical mode is intermediate between them. In the paper, the condition of the critical regime is obtained in the form of an asymptotic representation of the corresponding value of the system parameter reflecting the heat loss from the reaction phase.