Conditional Lie–Bäcklund symmetries and differential constraints for inhomogeneous nonlinear diffusion equations due to linear determining equations

The method of linear determining equations is developed to study conditional Lie–Bäcklund symmetries for evolution equations, which is more general than the classical determining equations for Lie's generators. As an application of this approach, the complete classification is presented for the inhomogeneous nonlinear diffusion equations which admit the second-order and third-order conditional Lie–Bäcklund symmetries. Several examples are given to illustrate the corresponding symmetry reductions due to the compatibility of the invariant conditions and the governing equations.