Exact solutions and generalized conditional symmetries to (n+1)-dimensional nonlinear diffusion equations with source term

It is shown that the (n+1)-dimensional nonlinear diffusion equations with source term admit a class of second-order generalized conditional symmetry depending on the space variable. Symmetry reductions and exact solutions are obtained through the generalized conditional symmetry approach. The results extend some known exact solutions such as the instantaneous source solution, dipole solution and certain polynomial type solutions of nonlinear diffusion equations without source.