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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/16833 |
| Date | 30 January 2015 |
| Creators | Mindu, Nkululeko |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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