Journal of Applied Mathematics
Volume 2013 (2013), Article ID 258528, 8 pages
Research Article

Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

Centre for Differential Equations, Continuum Mechanics and Applications and School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa

Received 29 December 2012; Accepted 1 March 2013

Academic Editor: Fazal M. Mahomed

Copyright © 2013 N. Mindu and D. P. Mason. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, other Lie point symmetries provided the permeability is either a power law or an exponential law of the voidage or is a constant. A rarefactive solitary wave solution of the partial differential equation is derived in the form of a quadrature for the exponential law for the permeability.