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非线性扩散方程的精确解

ISSN号：1005-3085
期刊名称：《工程数学学报》
时间：0
分类：O175.29[理学—数学;理学—基础数学]
作者机构：[1]西北工业大学应用数学系,西安710072, [2]宝鸡文理学院数学系,宝鸡721013
相关基金：Foundation item： The Natural Science Foundation of China （10472091; 10332030; 10502042）; the Key Scientific Research Plan Project of Baoji University of Arts and Sciences （ZK08103）.

关键词：推广旋转群, 推广伸缩群, 精确解, 非线性扩散方程, extended rotation group, extended scaling group, exact solution, nonlinear diffusion equation

中文摘要：

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。

英文摘要：

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.

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