Statistical model of the thermal ignition of a distributed system

This work is concerned with the instability of combustible mixtures against finite-amplitude nucleus-like fluctuations of temperature that lead to a stochastic thermal ignition. The phenomenon is associated with the presence of a potential barrier that must be crossed by nuclei to initiate the stochastic ignition, which turns out to be possible even under the deterministic explosion limit given by the well-known Frank-Kamenetskii model. A stochastic analysis of such phenomena has been given using a functional Fokker-Planck equation. The following discussion of the ignition is restricted to a one-dimensional case when the consumption of reactant is not taken into account. The results obtained here may be applied only to weak fluctuations