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

N. Mindu and D. P. Mason

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/258528

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:258528

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