有源非线性热方程的广义变量分离精确解

IF 0.5 4区数学 Q3 MATHEMATICS

Ukrainian Mathematical Journal Pub Date : 2024-08-16 DOI:10.1007/s11253-024-02316-9

Anatolii Barannyk, Tetyana Barannyk, Ivan Yuryk

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引用次数: 0

摘要

我们基于经典的变量分离法、变量分离法的广义化和还原法，提出了一种构建有源非线性热方程精确解的方法。我们考虑了将非线性热方程简化为常微分方程和两个常微分方程系的替代方法。分析方程的精确解类是通过广义变量分离法构建的。

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Exact Solutions with Generalized Separation of Variables of the Nonlinear Heat Equation with a Source

We propose a method for the construction of exact solutions to the nonlinear heat equation with a source based on the classical method of separation of variables, its generalization, and the method of reduction. We consider substitutions reducing the nonlinear heat equation to ordinary differential equations and to a system of two ordinary differential equations. The classes of exact solutions of the analyzed equation are constructed by the method of generalized separation of variables.

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来源期刊

Ukrainian Mathematical Journal MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

107

审稿时长

4-8 weeks

期刊介绍： Ukrainian Mathematical Journal publishes articles and brief communications on various areas of pure and applied mathematics and contains sections devoted to scientific information, bibliography, and reviews of current problems. It features contributions from researchers from the Ukrainian Mathematics Institute, the major scientific centers of the Ukraine and other countries. Ukrainian Mathematical Journal is a translation of the peer-reviewed journal Ukrains’kyi Matematychnyi Zhurnal, a publication of the Institute of Mathematics of the National Academy of Sciences of Ukraine.