GROUP CLASSIFICATION AND SYMMETRY REDUCTIONS OF THE NONLINEAR DIFFUSION CONVECTION EQUATION U(T)=(D(U)U(X))(X)-K'(U)U(X)

A non-linear diffusion-convection equation arising from the theory of transport in porous media is analyzed using the Lie group technique. A complete classification of the functional forms of the transport coef ficients is presented for which different symmetry groups are admitted . For a number of interesting cases, symmetry reductions are performed leading to exact group-invariant solutions. In particular, the specia l case of the (integrable) Fokas-Yortsos equation is examined in the l ight of the ''Painleve conjecture'' concerning the symmetry reductions of integrable PDEs.