拟线性热方程的函数分离变量解

Functional separable solutions to quasi-linear heat equation

用群状结构法研究拟线性热方程的分离变量解,对于允许和型分离变量解的二阶拟线性热方程给出了一个完整的分类.说明了一些带有函数类型反应项的方程具有函数分离变量解,推广了前人的结论.

In this paper, we considered the separable solutions to the quasi-linear heat equation with the group foliation method. A classification was carried out for the second order heat equations which admit additive separable solutions. The result is an extension of some known conclusions about the functional separation of variable solutions.