Abstract
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.