On exact solutions for nonlinear diffusion with source term (Q1860749)

This paper deals with the nonlinear diffusion equation and source term with power-law dependence forms. The author obtains simple exact solutions, which are derived by suitable transformations and standard techniques for an arbitrary number of dimensions \(n\geq 0\). Here \(n=0,1\) and 2 corresponds to the slab, cylinder and sphere, respectively. The author shows that some of the solutions obtained in the paper exhibit uniqueness, multiplicity and the phenomenon of singularity, criticality, oscillation, extinction and blow up.