带源项的变系数非线性反应扩散方程的精确解

本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)u_t=(g(x)D(u)u_x)_x+h(x)P(u)u_x+q(x)Q(u)进行研究. 当扩散项D(u)取u^m (m≠-1,0,1)和e^u两种重要情形时， 对该方程进行对称约化，得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解. 关键词： 广义条件对称 精确解 非线性反应扩散方程

Exact solutions to the nonlinear diffusion-convection equation with variable coefficients and source term

The nonlinear diffusion-convection equation f(x)u_t=(g(x)D(u)u_x)_x+h(x)P(u)u_x+q(x)Q(u) with variable coefficients and source term has been studied. This equation is symmetrically reduced by the generalized conditional symmetry method. Some exact solutions to the resulting equations are constructed, with the diffusion terms D(u)=u^m (m≠-1,0,1) and D(u)=e^u. These exact solutions are also the generalized functional separable solutions. Solutions to the equation with constant coefficients are covered by those exact solutions to the equation with variable coefficients.
Keywords： generalized conditional symmetry exact solution the nonlinear diffusion-convection equation