Geodesic
Application of generalized Bers degrees, the matrix method, and the Fourier method for solving the nonstationary heat equation in a multilayer medium
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 50-59

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In this paper, we present an analytical method for solving the nonstationary heat equation in a multilayer medium without internal sources based on generalized Bers degrees, the matrix method, and the Fourier method. We propose an algorithm for solving this problem for various geometries of a multilayer medium (plane layers and layers with axial and central symmetry). Using this algorithm, we give examples for three-layer plane and axisymmetric structures.
Keywords: multilayer medium, matrix method, heat conduction problem, generalized Bers degree, Fourier method. 
@article{INTO_2021_199_a5,
     author = {V. V. Kalmanovich and M. A. Stepovich},
     title = {Application of generalized {Bers} degrees, the matrix method, and the {Fourier} method for solving the nonstationary heat equation in a multilayer medium},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {50--59},
     publisher = {mathdoc},
     volume = {199},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_199_a5/}
}
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V. V. Kalmanovich; M. A. Stepovich. Application of generalized Bers degrees, the matrix method, and the Fourier method for solving the nonstationary heat equation in a multilayer medium. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 1, Tome 199 (2021), pp. 50-59. http://geodesic.mathdoc.fr/item/INTO_2021_199_a5/