非线性扩散方程的广义条件对称和精确解

Generalized conditional symmetries of nonlinear diffusion equation and exact solutions

应用广义条件对称方法研究非线性扩散方程的精确解.对容许广义条件对称约化的方程的反应系数和热源项的形式进行了分类,进而给出方程的精确解.相对于古典对称或条件对称方法,广义条件对称法给出了方程新的精确解.

The exact solutions of nonlinear diffusion equation was investigated by using of generalized conditional symmetries. A classification of the reaction coefficients and source terms is given when the equation admits generalized conditional symmetry, then the exact solutions are given. Compared with classical symmetry or the conditional symmetry method, the new solutions can be obtained via generalized conditional symmetries method.