Geodesic
On the matrix method for solving heat conduction problems in a multilayer medium in the presence of phase transitions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 30-37.

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The work is devoted to the applicability of the matrix method for solving the heat equation for multilayer media in the case where a phase transition is possible in some layer. We consider only stationary processes in the absence of internal heat sources. We propose a general method for layer systems with translation, axial, or central symmetry by using the technique of generalized Bers degrees. By the method indicated above, we perform calculations for one substance, when after a phase transition, the system becomes a two-layer system. We consider the dependence of the coordinate of the phase-transition point on the external temperature and compare results obtained for media with types of symmetry indicated above. A temperature field is constructed for multilayer media with various types of symmetry when a phase transition has occurred in a certain layer.
Keywords: mathematical model, matrix method, heat equation, multilayer medium, phase transition. 
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Yu. A. Gladyshev; V. V. Kalmanovich. On the matrix method for solving heat conduction problems in a multilayer medium in the presence of phase transitions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 3, Tome 172 (2019), pp. 30-37. http://geodesic.mathdoc.fr/item/INTO_2019_172_a2/

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