Mp. Edwards et P. Broadbridge, EXACT TRANSIENT SOLUTIONS TO NONLINEAR DIFFUSION CONVECTION EQUATIONSIN HIGHER DIMENSIONS, Journal of physics. A, mathematical and general, 27(16), 1994, pp. 5455-5465
The complete Lie algebra of classical infinitesimal symmetries of the
nonlinear diffusion-convection equation in two and three dimensions is
presented. Except for some cases involving constant diffusivity, a co
mplete reduction to an ordinary differential equation is not possible.
However, closed-form solutions are obtained for special forms of both
the 2D and 3D nonlinear diffusion-convection equations, using a symme
try reduction and an additional physical constraint, This extends the
small list of closed-form transient solutions already known.