Thesis (Ph.D.) - University of Queensland, 2003. / Includes bibliography.

Thesis--Lund. / Extra t.p., with thesis note inserted. Imprint on cover: Lund, C.W.K. Gleerup. "A study of problems connected with Riesz' generalization of the Riemann-Liouville integral."--Introd. "References": p. [98].

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains ix, 134 p.; also includes graphics. Includes bibliographical references (p. 130-134). Available online via OhioLINK's ETD Center

Thesis (PhD.(Mathematics))-University of Pretoria, 2005. / Includes bibliographical references. Available on the Internet via the World Wide Web.

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2007. / Includes bibliographical references (leaves 72-85). Also available in electronic version.

Thesis (M.Eng.)(Mechanical)--University of Pretoria, 2006. / Includes summary. Includes bibliographical references. Available on the Internet via the World Wide Web.

Thesis (MSc (Applied Mathematics))--Stellenbosch University, 2008. / The Korteweg-de Vries (KdV) hierarchy is an important class of nonlinear evolution equa- tions with various applications in the physical sciences and in engineering. In this thesis analytical solution methods were used to ¯nd exact solutions of the third and ¯fth order KdV equations, and numerical methods were used to compute numerical solutions of these equations. Analytical methods used include the Fan sub-equation method for constructing exact trav- eling wave solutions, and the simpli¯ed Hirota method for constructing exact N-soliton solutions. Some well known cases were considered. The Fourier spectral method and the ¯nite di®erence method with Runge-Kutta time dis- cretisation were employed to solve the third and the ¯fth order KdV equations with periodic boundary conditions. The one soliton and the two soliton solutions were used as initial conditions. The numerical solutions are obtained and compared with the exact solutions. The propagation of a single soliton as well as the interaction of double soliton solutions is modeled well by both numerical methods, although the Fourier spectral method performs better. The stability, consistency and convergence of these numerical methods were investigated. Error propagation is studied. The theoretically predicted quadratic convergence of the ¯nite di®erence method as well as the exponential convergence of the Fourier spectral method is con¯rmed in numerical experiments.

Made available in DSpace on 2014-08-27T14:36:46Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-09-16Bitstream added on 2014-08-27T15:57:18Z : No. of bitstreams: 1 000722977.pdf: 686481 bytes, checksum: 12d3608646823cdd7066cbaaae5388ee (MD5) / Neste trabalho estudamos problemas elípticos do seguinte tipo: (P) Lu+V(x)|x|?ap* |u|p?2u = K(x)|x|?ap* f(u), em RN, em que V,K :RN ? R são potenciais não negativos que podem tender a zero no in?nito, f :RN ?R tem crescimento subcrítico e Lu é um operador elíptico. Quando Lu é o operador p-Laplaciano com peso, isto é, Lu = Lapu = ?div(|x|?ap|?u|p?2?u), provamos resultados de existência de solução positiva para K(x) ? 1 em RN e de solução positiva de energia mínima para K podendo tender a zero no in?nito. No primeiro caso a técnica é baseada num argumento de truncamento, introduzido por del Pino e Felmer em [34] e usado por Alves e Souto em [10], que nos permite uma abordagem variacional. No segundo caso, usamos novamente a abordagem variacional e o principal argumento, usado por Alves e Souto em [11], é considerar convenientes condições de crescimento sobre os potenciais para obter imersões compactas no espaço todo. Esta última técnica foi adaptada para obter resultados de existência de solução de energia mínima não trivial para o operador Lu = ?2u = ?(?u) / In this work we studied elliptic problems of the following type: (P) Lu+V(x)|x|?ap* |u|p?2u = K(x)|x|?ap* f(u), em RN, em que V,K :RN ? R are nonnegative potentials that can vanish at in?nity, f :RN ?R has a subcritical growth and Lu is an elliptic operator. When Lu is the weighted p-laplacian operator, namely, Lu = Lapu = ?div(|x|?ap|?u|p?2?u), we prove existence results of positive solution for K(x) ? 1 in RN and positive ground state solution for the case when K may tend to zero in in?nity. In the ?rst case the technique is a truncation argument, introduced by del Pino and Felmer, in [34], and used by Alves and Souto, in [10], that allows us to use a variational approach. In the second case, we also use the variational approach and the main argument, used by Alves and Souto, in [11], is to consider suitable growth conditions on the potentials to obtain compact embedded in the whole space. This last technique was adapted to obtain existence of nontrivial ground state solution for operator Lu = ?2u = ?(?u)

No description available.

The purpose of this paper is to develop a general method for using Finite Elements in the Steepest Descent Method. The main application is to a partial differential equation for a Transonic Flow Problem. It is also applied to Burger's equation, Laplace's equation and the minimal surface equation. The entire method is tested by computer runs which give satisfactory results. The validity of certain of the procedures used are proved theoretically. The way that the writer handles finite elements is quite different from traditional finite element methods. The variational principle is not needed. The theory is based upon the calculation of a matrix representation of operators in the gradient of a certain functional. Systematic use is made of local interpolation functions.