Group classification and exact solutions of a radially symmetric porous-medium equation

In this paper we perform a group classification for the generalized radial porous-medium equation. We also classify symmetry reductions of the equatio n to first- or second-order ordinary differential equations (ODEs) and henc e construct invariant solutions in a systematic manner. We show that the re duced second-order equations are invariant under either a two-parameter or one-parameter Lie groups. In the first case, they are completely integrated by a pair of quadratures, In the latter, they are often reduced to first-o rder ODEs of Abel type. (C) 2001 Elsevier Science Ltd. All rights reserved.