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

Gungor F.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol.37, no.2, pp.245-255, 2002 (SCI-Expanded) identifier identifier


In this paper we perform a group classification for the generalized radial porous-medium equation. We also classify symmetry reductions of the equation to first- or second-order ordinary differential equations (ODEs) and hence construct invariant solutions in a systematic manner. We show that the reduced 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-order ODEs of Abel type. (C) 2001 Elsevier Science Ltd. All rights reserved.