Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity
The derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vec...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/585167 |
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| _version_ | 1849304669727227904 |
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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 derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves. |
| format | Article |
| id | doaj-art-41d7c66aa00840a8b90f2407c5ec8d7c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-41d7c66aa00840a8b90f2407c5ec8d7c2025-08-20T03:55:40ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/585167585167Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and ViscosityN. Mindu0D. P. Mason1Programme for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South AfricaProgramme for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South AfricaThe derivation of conservation laws for the magma equation using the multiplier method for both the power law and exponential law relating the permeability and matrix viscosity to the voidage is considered. It is found that all known conserved vectors for the magma equation and the new conserved vectors for the exponential laws can be derived using multipliers which depend on the voidage and spatial derivatives of the voidage. It is also found that the conserved vectors are associated with the Lie point symmetry of the magma equation which generates travelling wave solutions which may explain by the double reduction theorem for associated Lie point symmetries why many of the known analytical solutions are travelling waves.http://dx.doi.org/10.1155/2014/585167 |
| spellingShingle | N. Mindu D. P. Mason Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity Abstract and Applied Analysis |
| title | Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity |
| title_full | Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity |
| title_fullStr | Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity |
| title_full_unstemmed | Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity |
| title_short | Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity |
| title_sort | derivation of conservation laws for the magma equation using the multiplier method power law and exponential law for permeability and viscosity |
| url | http://dx.doi.org/10.1155/2014/585167 |
| work_keys_str_mv | AT nmindu derivationofconservationlawsforthemagmaequationusingthemultipliermethodpowerlawandexponentiallawforpermeabilityandviscosity AT dpmason derivationofconservationlawsforthemagmaequationusingthemultipliermethodpowerlawandexponentiallawforpermeabilityandviscosity |