Methods for solving problems on thermal conductivity of multilayer media in the presence of heat sources

The solution of problems on phase transitions in multilayer media when they are heated is of practical interest owing to the increasing use of multilayer materials in engineering and construction under various temperature conditions. In this paper, we assume that the medium contains distributed heat sources caused by physical or chemical processes, which can lead to phase transitions. We describe the method of generalized Bers degrees and the matrix method for solving the heat conduction problem in multilayer media and for the search for boundaries of phase transitions.