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

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.