非线性扩散方程的精确解(英文)

Exact Solutions for the Nonlinear Diffusion Equation

本文研究非线性扩散方程的精确解,文中分别给出非线性扩散方程在推广旋转群和推广伸缩群上不变时满足的条件,并且利用推广旋转群和推广伸缩群构造方程的精确解,最后,给出了非线性扩散方程在推广旋转伸缩群上不变时满足的条件,推广旋转伸缩群也被用来构造非线性扩散方程的精确解。

In this paper, we study exact solutions to nonlinear diffusion equations. We formulate conditions for the nonlinear diffusion equation which is invariant under the extended rotation group and the extended scaling group, respectively. Meanwhile, we construct exact solutions to nonlinear diffusion equations by using the extended rotation group and the extended scaling group. Finally, we formulate conditions for nonlinear diffusion equation which is invariant under the extended rotation-scaling group, the extended rotation-scaling group is also used to construct exact solutions to the nonlinear diffusion equation.