Symmetry reductions for a nonlinear diffusion-absorption equation in two spatial dimensions

Departamento de Matemáticas, Universidad de Cádiz P.O.Box 40, 11510 Puerto Real, Cádiz, Spain

Received: 6 January 1998
Accepted: 4 May 1998

Abstract

The complete Lie algebra of classical infinitesimal symmetries of the nonlinear two-dimensional (2D) diffusion-absorption equation is presented. The functional forms of absorption for which the two-dimensional diffusion-absorption equation can be fully reduced to an ordinary differential equation by classical Lie simmetries are derived. The two-dimensional optimal system is used to generate some new reductions of the 2D partial differential equation to ordinary differential equations. Some of these ordinary differential equations can be interpreted in terms of finite-time blow-up processes for the radial and the one-dimensional problem.