Geodesic
On the solution of the heat-conduction problem in a multilayer medium with phase transitions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 46-54

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In this paper, the stationary problem of heat conduction is solved for the case of a multilayer medium consisting of two materials. In the problem considered, the heat sources are located in a layer in which phase transitions cannot occur, and the neighboring layer is heated only due to thermal conductivity and a phase transition is possible in it. To solve the problem of heat conduction and to determine the coordinates of the points of phase transition, the matrix method is used together with the techniques of generalized Bers degrees. The temperature field is constructed for multilayer media with various types of symmetry, when a phase transition has occurred in some layer.
Keywords: mathematical model, matrix method, heat-conduction equation, multilayer medium
Mots-clés : phase transition. 
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     title = {On the solution of the heat-conduction problem in a multilayer medium with phase transitions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     volume = {192},
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Yu. A. Gladyshev; V. V. Kalmanovich. On the solution of the heat-conduction problem in a multilayer medium with phase transitions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Tome 192 (2021), pp. 46-54. http://geodesic.mathdoc.fr/item/INTO_2021_192_a4/