Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source u_t=(A(u)u_x)_x+∈B(u,u_x). A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approximate solutions to the resulting perturbed equations are constructed via examples.