广义条件对称和变系数非线性扩散方程的解  

Generalized conditional symmetry and solutions to nonlinear diffusion equations with variable coefficients

作　　者：万晖[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《陕西师范大学学报（自然科学版）》2012年第5期14-17,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11001220);陕西省教育厅科学研究计划项目(2010JK866)

摘　　要：利用广义条件对称方法研究了一类变系数非线性扩散方程.当扩散项取D(u)=um(m≠-1,0,1)时,对该方程进行分类讨论,得到了该方程的一些精确解,这些精确解是泛函分离变量形式的解,它们可看作是广义泛函分离变量解的特殊形式.这些精确解有丰富的理论及实践意义,且深化和发展了此类方程的解的范畴.Using generalized conditional symmetry method to research a kind of nonlinear diffusion equations with variable coefficients.When the diffusion term is taken in the form D（u）=um（m≠-1,0,1）,this equation is discussed,some exact solutions to the equation are obtained.The exact solutions are the solutions of the functional separation of variables in the form,they can be seen as a special form of generalized functional separation of variables solutions.These exact solutions have a rich theoretical and practical significance,and deepen and develop the scope of solutions of such equation.

关 键 词：广义条件对称 精确解 变系数非线性扩散方程 

分 类 号：O175.29[理学—数学]