3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item An inverse problem for an inhomogeneous string with an interval of zero density and a concentrated mass at the end point(2016-05-10) Mdhluli, Daniel SiphoThe direct and inverse spectral problems for an inhomogeneous string with an interval of zero density and a concentrated mass at the end point moving with damping are investigated. The partial differential equation is mapped into an ordinary differential equation using separation of variables which in turn is transformed into a Sturm-Liouville differential equation with boundary conditions depending on these parathion variable. The Marchenko approach is employed in the inverse problem to recover the potential, density and other parameters from the knowledge of the two spectra and length of the string.Item Potential flows and transformation groups(2014-03-04) Pereira, Kevin PaulIn this work we will consider the steady and two-dimensional potential flow of an incompressible fluid past a body without friction. Contrary to common experience, we will show that it is possible to calculate the Lie point symmetries that will leave the boundary value problem invariant. We are able to do this by solving the determining equation for the Lie point symmetries subject to a side condition. The side condition is a consequence of the boundary condition that occurs in the boundary value problem. We will show that solutions of the boundary value problem that were obtained previously using the method of conformal transformations are also group invariant solutions of the boundary value problem. We will also show that every group invariant solution of the boundary value problem can be used to generate new group invariant solutions of the same boundary value problem.