带有扰动非线性源的多孔介质方程的近似泛函分离变量

摘要

讨论了带有扰动非线性源的多孔介质方程的近似泛函分离变量问题．给出了该类方程容许近似泛函分离变量解的完全分类．举例阐述了近似泛函分离变量解的求解步骤，获得了分类方程的近似泛函分离变量解．%The approximate functional variable separation for the porous medium equation with perturbed nonlinear source is studied. Complete classification of the perturbed equation which admits approximate functional separable solutions is obtained. The main solving procedure foe the approximate functional variable separation approach is shown by way of examples, and the corresponding approximate functional separable solutions to the resulting equations are then constructed.