Solution of the thermoelasticity problem in the form of a traveling wave and its application to analysis of possible regimes of solid-phase transformations

Using the known self-similar solutions of the theory of temperature stresses and thermal theory of combustion on the basis of coupled models of solid-phase combustion proposed for the description of various physicochemical transformations, it is shown that the regime of fast (supersonic) solid-phase transformation (solid-phase detonation) is typical of a reacting medium, as well as the regime of slow combustion. Partial (exact) integration and transformation of variables allow one to reduce the systems of equations that describe various solid-phase processes to shock-wave equations having continuous solutions of the traveling-wave type.