Conditional Lie-Backlund Symmetries and Functionally Generalized Separation of Variables to Quasi-Linear Diffusion Equations with Source

The conditional Lie-Backlund symmetry method is applied to investigate the functionally generalized separation of variables for quasi-linear diffusion equations with a source. The equations and the admitted conditional Lie-Backlund symmetries related to invariant subspaces are identified. The exact solutions possessing the form of the functionally generalized separation of variables are constructed for the resulting equations due to the corresponding symmetry reductions.