Conditional Lie–Bäcklund symmetries and functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations

The functionally separable solutions of the generalized inhomogeneous nonlinear diffusion equations are studied by applying the conditional Lie–Backlund symmetry method. A complete list of canonical forms for such equations are presented. Exact solutions to the resulting equations are constructed. The asymptotic behaviors and blow-up properties of some solutions are also discussed.