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The purpose of this research is the development of a method for studying a two-dimensional semi-linear elliptic partial differential equation in an infinite stripe with slow variations of one of the boundaries. The problem is reformulated as a boundary value problem for a semi-linear elliptic equation with a small parameter at one higher derivative (the singular perturbation parameter). The method is based on the boundary function of Tikhonov, shaped by Vasil'eva and Butuzov for a one-dimensional case. The developed method has clear parallels with the one-dimensional boundary function method. / Thesis (PhD)--University of South Australia, 2006.

We examine the boundary-layer flow of generalised Newtonian fluids. A specific member of this class of non-Newtonian fluids, namely the Ostwald-de Waele or power-law fluid, is studied in some detail. We show, through the numerical solution of the governing equations, that this empirical model of fluids encountered in physical and industrial situations is of limited benefit when considering the boundary-layer flow of such a fluid. We then develop and employ a Carreau viscosity model in the same context and show that the numerical marching scheme has better convergence behaviour than was the case for power-law fluids. We also investigate the boundary-layer flow of a Newtonian fluid over a thin film of non-Newtonian fluid, described by a Carreau fluid model, by focusing specifically on similarity-type solutions. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1456589 / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2009

The purpose of this research is the development of a method for studying a two-dimensional semi-linear elliptic partial differential equation in an infinite stripe with slow variations of one of the boundaries. The problem is reformulated as a boundary value problem for a semi-linear elliptic equation with a small parameter at one higher derivative (the singular perturbation parameter). The method is based on the boundary function of Tikhonov, shaped by Vasil?eva and Butuzov for a one-dimensional case. The developed method has clear parallels with the one-dimensional boundary function method.

Thesis (Ph.D.)--University of Tulsa, 1990. / Includes bibliographical references (leaves 204-209).

Thesis (Ph.D.) -- Adelaide University, Dept. of Physics and Mathematical Physics, 2001. / Includes a copy of an article co-authored by the author during the preparation of this thesis. Bibliography: leaves 253-266. Also available electronically.

Thesis (Ph.D.) -- Adelaide University, Dept. of Physics and Mathematical Physics, 2001. / Bibliography: leaves 253-266. Also available in print form.

Thesis (Ph.D.)--Australian National University, 2003.

Thesis (M. App. Sc.)--Carleton University, 2004. / Includes bibliographical references (p. 131-139). Also available in electronic format on the Internet.

Thesis (Ph.D.) - Carleton University, 2005. / Includes bibliographical references (p. 295-301). Also available in electronic format on the Internet.