The paper considers the solution of a one-dimensional homogeneous equation of heat conduction in a multilayer. In this paper, the orthogonality of the obtained eigenfunctions is proved.
heat conduction equation, matrix method, multilayer medium, imperfect thermal contact.
1. CARSLAW, H. S., JAEGER, J. C. (1959) Conduction of Heat in Solids. Oxford: Oxford University Press.
2. STEPOVICH, M. A., KALMANOVICH, V. V. & SEREGINA, E. V. (2020) Possibility of applying the matrix method to modeling the cathodoluminscescence caused by a wide electron beam in a planar multilayer semiconductor structures. Bulletin of the Russian Academy of Sciences: Physics. 84(5). p. 576-579.
3. KALMANOVICH, V. V., SEREGINA, E. V. & STEPOVICH, M. A., (2020) Mathematical modeling of heat and mass transfer phenomena caused by interaction between electron beams and planar semiconductor multilayers. Bulletin of the Russian Academy of Sciences: Physics. 84 (7). p. 844-850.
4. KALMANOVICH, V. V., KARTANOV, A. A. & STEPOVICH, M. A. (2021) On some problems of modelling the non-stationary heat conductivity process in an axisymmetric multilayer medium. Journal of Physics: Conference Series. 1902. p. 6012073.
5. BERS, L. & GELBART, A. (1944) On a class of functions defined by partial differential equations. Transactions of the American Mathematical Society. 56. p. 67-93.
6. GLADYSHEV, Yu A. (1994) On a sequence of generalized Bers exponential functions with inte-rior structure Mathematical Notes. Mathematical Notes. 55 (3). p. 251-261.
7. GOLUBKOV, A. A. (2019) A boundary value problem for the Sturm-Liouville equation with piecewise entire potential on the curve and solution discontinuity conditions. Siberian Electronic Mathematical Reports. 16. p. 1005-1027.
