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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/258528 |
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| _version_ | 1832552455226785792 |
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| author | N. Mindu D. P. Mason |
| author_facet | N. Mindu D. P. Mason |
| author_sort | N. Mindu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-afdc6ca4395c4ae49cc1e9de8258c18e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-afdc6ca4395c4ae49cc1e9de8258c18e2025-02-03T05:58:44ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/258528258528Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group AnalysisN. Mindu0D. P. Mason1Centre 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 AfricaCentre 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 AfricaThe 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.http://dx.doi.org/10.1155/2013/258528 |
| spellingShingle | N. Mindu D. P. Mason Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis Journal of Applied Mathematics |
| title | Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis |
| title_full | Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis |
| title_fullStr | Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis |
| title_full_unstemmed | Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis |
| title_short | Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis |
| title_sort | permeability models for magma flow through the earth s mantle a lie group analysis |
| url | http://dx.doi.org/10.1155/2013/258528 |
| work_keys_str_mv | AT nmindu permeabilitymodelsformagmaflowthroughtheearthsmantlealiegroupanalysis AT dpmason permeabilitymodelsformagmaflowthroughtheearthsmantlealiegroupanalysis |