Group Classification and Generalized Conditional Symmetry Reduction of the Nonlinear Diffusion–Convection Equation with a Nonlinear Source

The generalized conditional symmetry method, which can be considered a generalization of the conditional symmetry method, is used to study the nonlinear diffusion–convection equations with a nonlinear source. In particular, exponential and power law diffusivities are examined and we obtain mathematical forms of the convective term and the source term, which permit the generalized conditional symmetry reductions. A number of examples are considered and some exact solutions are constructed via the compatibility of the generalized conditional symmetry and the considered equation.