Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis
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 s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/258528 |
| Summary: | 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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| ISSN: | 1110-757X 1687-0042 |