非线性热传导方程的对称性分类
Symmetry Classification for the Nonlinear Heat Conductivity Equation
摘要：
本文研究了一般形式的非线性热传导方程$u_t = [E(x, u)u_x]_x + H(x, u)$的对称性。这些方程的点对称性分析被认为是以及一个等价的分类，其中承认的主要李代数的一维扩展。给出了非线性热传导方程的等价变换的不变解，并对附加算子的非线性热传导方程进行了分类。
英文摘要：
In this investigation, symmetry properties of the nonlinear heat conductivity equations of general form $u_t = [E(x, u)u_x]_x + H(x, u)$ are studied. The point symmetry analysis of these equations is considered as well as an equivalence classification which admits an extension by one dimension of the principal Lie algebra of them. The invariant solutions of equivalence transformations and classification of the nonlinear heat conductivity equations among with additional operators are also given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
