Behavior of the temperature and burnup of a reactive body at the surface $x=0$ upon thermal ignition

Using the Laplace transform, we show that equations that govern the evolution with time of the temperature and burnup of areactive body in the cross section $x=0$ in the processes of thermal ignition can be derived. The equations for the temperature and burnup of a semibounded body at the ignition point $x=0$ are obtained when the ignition is initiated by a radiation flux and in the case of thermal explosion, of a hot spot. An asymptotic analysis of the equations obtained is carried out, and the ignition times of bodies and the critical conditions for ignition of a hot spot are determined. Vilyunov's “adiabatic method” of obtaining the temporal ignition characteristics is justified. The results of the asymptotic analysis of the ignition of a hot-spot are supported.