Exact polynomial solutions to some nonlinear diffusion equations (Q2366477)

For certain nonlinear diffusion equations given by \(\partial u/\partial t =\nabla (D(u)\nabla u)\) a class of non-group-invariant exact solutions is constructed. The approach adopted throughout the paper is based on seeking changes of variables which lead to solutions which are polynomials in the spatial variables. The method is applicable to equations which may be written in an appropriate quadratically nonlinear form. There are many examples given.