The new model ideas in the problem of thermal shock

We have investigated the problem of thermal shock of a semi-half-space with moving boundary in the conditions of sharp temperature heating, thermal heating, heating by environment. The dangerous heating regime is found. We have obtained new integral equations that reduce the considered problem to finding the corresponding Green-function; that is much simpler. We have developed the new mathematical theory for the domains which boundaries move with the constant velocity by modification of the thermal potentials method.