二维热传导方程的非古典对称和相容性

Nonclassical symmetries and compatibility of two-dimensional heat equation

研究了二维热传导方程的非古典对称的决定方程,对于一般的一维偏微分方程,运用向量场的延拓和不变表面条件及初始方程的相容性两种方法得出了相同的非古典对称的决定方程.由此,得到了利用不变条件及初始方程的相容性也可求得非线性偏微分方程的非古典对称的决定方程的重要结论.最后,将此结论推广到二维热传导方程,证明了该结论对于二维热传导方程也是可行的.

The determining equations for the nonclassical symmetries of the two-dimensional heat equation are studied. A simple partial differential equation is quoted. It is concluded that the nonclassical symmetries of the nonlinear partial differential equations can be derived by using the compatibility between the original equation and the invariant surface condition. Finally, the conclusion is used to discuss the two-dimensional heat equation.