Solitary wave solutions for the magma equation: symmetry methods and conservation laws
A dissertation submitted for the degree of Masters of Science, School of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, 2014. === The magma equation which models the migration of melt upwards through the Earth’s mantle is considered. The magma equation depends on...
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ndltd-netd.ac.za-oai-union.ndltd.org-wits-oai-wiredspace.wits.ac.za-10539-168332019-05-11T03:42:07Z Solitary wave solutions for the magma equation: symmetry methods and conservation laws Mindu, Nkululeko Magmas. Symmetry. Conservation laws. A dissertation submitted for the degree of Masters of Science, School of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, 2014. The magma equation which models the migration of melt upwards through the Earth’s mantle is considered. The magma equation depends on the permeability and viscosity of the solid mantle which are assumed to be a function of the voidage . It is shown using Lie group analysis that the magma equation admits Lie point symmetries provided the permeability and viscosity satisfy either a power law, or an exponential law for the voidage or are constant. The conservation laws for the magma equation for both power law and exponential law permeability and viscosity are derived using the multiplier method. The conserved vectors are then associated with Lie point symmetries of the magma equation. A rarefactive solitary wave solution for the magma equation is derived in the form of a quadrature for exponential law permeability and viscosity. Finally small amplitude and large amplitude approximate solutions are derived for the magma equation when the permeability and viscosity satisfy exponential laws. 2015-01-30T11:00:24Z 2015-01-30T11:00:24Z 2015-01-30 Thesis http://hdl.handle.net/10539/16833 en application/pdf |
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en |
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Others
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Magmas. Symmetry. Conservation laws. |
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Magmas. Symmetry. Conservation laws. Mindu, Nkululeko Solitary wave solutions for the magma equation: symmetry methods and conservation laws |
description |
A dissertation submitted for the degree of Masters of Science, School of Computational and Applied Mathematics, University of Witwatersrand, Johannesburg, 2014. === The magma equation which models the migration of melt upwards through
the Earth’s mantle is considered. The magma equation depends on the permeability
and viscosity of the solid mantle which are assumed to be a function
of the voidage . It is shown using Lie group analysis that the magma equation
admits Lie point symmetries provided the permeability and viscosity satisfy
either a power law, or an exponential law for the voidage or are constant. The
conservation laws for the magma equation for both power law and exponential
law permeability and viscosity are derived using the multiplier method.
The conserved vectors are then associated with Lie point symmetries of the
magma equation. A rarefactive solitary wave solution for the magma equation
is derived in the form of a quadrature for exponential law permeability and viscosity.
Finally small amplitude and large amplitude approximate solutions are
derived for the magma equation when the permeability and viscosity satisfy
exponential laws. |
author |
Mindu, Nkululeko |
author_facet |
Mindu, Nkululeko |
author_sort |
Mindu, Nkululeko |
title |
Solitary wave solutions for the magma equation: symmetry methods and conservation laws |
title_short |
Solitary wave solutions for the magma equation: symmetry methods and conservation laws |
title_full |
Solitary wave solutions for the magma equation: symmetry methods and conservation laws |
title_fullStr |
Solitary wave solutions for the magma equation: symmetry methods and conservation laws |
title_full_unstemmed |
Solitary wave solutions for the magma equation: symmetry methods and conservation laws |
title_sort |
solitary wave solutions for the magma equation: symmetry methods and conservation laws |
publishDate |
2015 |
url |
http://hdl.handle.net/10539/16833 |
work_keys_str_mv |
AT mindunkululeko solitarywavesolutionsforthemagmaequationsymmetrymethodsandconservationlaws |
_version_ |
1719085028368973824 |