Conditional Lie-Bäcklund symmetries and functionally generalized separable solutions to the generalized porous medium equations with source

The functionally generalized separable solutions of the generalized porous medium equations with power law and exponential diffusivity are studied by using the conditional Lie-Bäcklund symmetry method. The variant forms of the considered equations, which admit the linear conditional Lie-Bäcklund symmetries, are identified. A number of examples are considered and some exact solutions, defined on the polynomial, trigonometric and exponential invariant subspaces determined by the linear conditional Lie-Bäcklund symmetries, are constructed.