带有热源项的非线性扩散方程的精确解Exact solutions of the nonlinear diffusion equations with source
姬利娜;冯玮;
摘要(Abstract)：
讨论了带有热源项的非线性扩散方程.通过一种直接简洁的方法得到了几种精确解.该方法可用于更高阶演化方程的求解问题。
关键词(KeyWords)： 非线性扩散方程;精确解;二维动力系统
基金项目(Foundation): 西北大学优秀博士论文资助项目(08YYB03);; 河南省教育厅自然科学研究资助计划项目(2008A110008);; 河南省2007年基础与前沿技术研究计划项目(072300410480)
作者(Authors): 姬利娜;冯玮;
参考文献(References)：
- [1]King J R.Some nonlocal transformations between nonlinear diffusion equations[J].J.Phys.A,1990,23:5441-5464.
- [2]Saied E A,EL-Rahaman R A.On the porous medium equation with modified Fourier’s law:symmetries andintegrability[J].J.Phys.Soc.Japan,1999,68:360-368.
- [3]Estevez P G,Qu C Z,Zhang S L.Separation of variables of a generalized porous medium equation withnonlinear source[J].J.Math.Anal.Appl.,2002,275:44-59.
- [4]Ji L N,Qu C Z.Conditional symmetries and solutions to a class of nonlinear diffusion-convection equations[J].Commun.Theor.Phys.,2006,46:668-674.
- [5]Qu C Z,Ji L N,Wang L Z.Conditional Lie B¨acklund symmetries and sign-invariants to quasi-linear diffusionequations[J].Stud.Appl.Math.,2007,119:355-391.
- [6]Qin M C,Fan G H.A new method for finding special solutions of nonlinear diffusion equation[J].NonlinearDyn.,2009,55:349-353.