On exact solutions for nonlinear diffusion with source term

Simple exact solutions are obtained for nonlinear diffusion and source term with power-law dependence forms. These solutions are derived by suitable transformations and standard techniques for an arbitrary. number of dimensions igreater than or equal to 0 with particular emphases on i = 0, 1 and 2 corresponding to the slab, cylinder and sphere respectively. The results obtained include, as special cases, some earlier known results; they also apply to numerous equations which have hitherto not been studied. Some of the solutions obtained also exhibit uniqueness, multiplicity and the phenomenon of singularity, criticality, oscillation, extinction and blow up. We show some of these phenomena graphically.