Abstract
The problem of constructing eigenfunctions of a one-dimensional thermoelastic operator in Cartesian, cylindrical, and spherical coordinate systems is considered. The corresponding Sturm–Liouville problem is formulated using Fourier’s separation of variables applied to a coupled system of thermoelasticity equations, assuming that the heat transfer rate is finite. It is shown that the eigenfunctions of the one-dimensional thermoelastic operator are expressed in terms of well-known trigonometric, cylinder, and spherical functions. However, coupled thermoelasticity problems are solved analytically only under certain boundary conditions, whose form is determined by the properties of the eigenfunctions.
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Funding
This work was supported by the Russian Science Foundation, project no. 23-21-00189, https://rscf.ru/en/project/23-21-00189/.
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Translated by I. Ruzanova
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Zemskov, A.V., Tarlakovskii, D.V. Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems. Comput. Math. and Math. Phys. 64, 401–415 (2024). https://doi.org/10.1134/S0965542524030175
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DOI: https://doi.org/10.1134/S0965542524030175