一维广义热传导方程的精确解

Exact Solutions of One-Dimensional General Heat Conduction Equation

【目的】为构造一维广义热传导方程新的精确解。【方法】利用李群分析法把一维广义热传导方程的解析求解问题约化为寻找常微分方程精确解的研究和探索问题。【结果】结合试探函数法和观察法给出了一维广义热传导方程的许多新的显式解析解和行波解。【结论】所得的新解析解扩展和完善了已有的结果。

[Purposes]The exact solutions of one-dimensional general heat conduction equation are constructed.[Methods]Searching for exact solutions of one-dimensional general heat conduction equation is reduced to study and find exact solutions of the corresponding to ordinary differential equation.[Findings]In addition,many new explicit analytical solutions and travelling wave solutions of one-dimensional general heat conduction equation are presented by use of the Lie group analysis method,transformation-trial function method and observational methods.[Conclusions]The new analytical solutions obtained here extend the existing study.