M.Sc. / In this dissertation, a symmetry analysis of a third order non-linear partial differential equation which describes the filtration of a non-Newtonian liquid in porous media is performed. A review of the derivation of the partial differential equation is given which is based on the Darcy Law. The partial differential equation contains a parameter n and a function f. We derive the Lie Point Symmetries of the partial differential equation for all cases of n and f. These symmetries are used to find the invariant solutions of the partial differential equation. We find that there is only one conservation law for the partial differential equation with f and n arbitrary and we prove that there is no potential symmetry corresponding to this conservation law for any case of n and f.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:2008 |
| Date | 06 February 2012 |
| Creators | Kartal, Ozgül |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
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