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

Abstract EN

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.