物理学报Issue(9)：18-26,9.DOI:10.7498/aps.62.090203
带源项的变系数非线性反应扩散方程的精确解*
Exact solutions to the nonlinear diffusion-convection equation with variable coefficients and source term∗
摘要
Abstract
The nonlinear diffusion-convection equation f(x)ut =(g(x)D(u)ux)x+h(x)P(u)ux+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)=um(m=−1,0,1) and D(u)=eu. 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.关键词
广义条件对称/精确解/非线性反应扩散方程Key words
generalized conditional symmetry/exact solution/the nonlinear diffusion-convection equation引用本文复制引用
万晖..带源项的变系数非线性反应扩散方程的精确解*[J].物理学报,2013,(9):18-26,9.基金项目
国家自然科学基金(批准号:10932002,11172120,11202090,10972127)资助的课题.@@@@Project supported by the National Natural Science Foundation of China (Grant Nos.10932002,11172120,11202090,10972127) （批准号:10932002,11172120,11202090,10972127）
