Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-04-22 DOI:10.1134/s0965542524030175

A. V. Zemskov, D. V. Tarlakovskii

引用次数: 0

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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笛卡尔、圆柱和球面坐标系中一维热弹性算子的 Sturm-Liouville 问题

摘要研究了在直角坐标系、圆柱坐标系和球面坐标系中构建一维热弹性算子特征函数的问题。假设热传导率是有限的，利用傅里叶变量分离法对热弹性方程耦合系统提出了相应的 Sturm-Liouville 问题。研究表明，一维热弹性算子的特征函数可以用众所周知的三角函数、圆柱函数和球面函数来表示。然而，耦合热弹性问题只能在某些边界条件下进行解析求解，这些边界条件的形式由特征函数的性质决定。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.