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2013 Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
N. Mindu, D. P. Mason
J. Appl. Math. 2013(SI27): 1-8 (2013). DOI: 10.1155/2013/258528


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.


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N. Mindu. D. P. Mason. "Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis." J. Appl. Math. 2013 (SI27) 1 - 8, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1266.86006
MathSciNet: MR3039733
Digital Object Identifier: 10.1155/2013/258528

Rights: Copyright © 2013 Hindawi


Vol.2013 • No. SI27 • 2013
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