In chapter 1, we focus on the full potential equation in an infinite nozzle with some decay cross-sections and prove the existence and stability of the transonic shock wave; which is a solution to a free boundary value problem for a quasi-linear mix-typed partial differential equation with the position of shock as a free boundary. To achieve this conclusion, we reduce it to a free boundary value problem for a quasi-linear elliptic equation in an unbounded domain. The crucial step in our analysis is to derive some uniform a priori estimates in such a domain. Then we apply the fixed point theorem to establish the existence of solutions to the full potential equation. / In chapter 2, we study the short time existence of discontinuous shock front solutions of the pressure gradient system which is the Euler system without inertial terms, where the initial data can have shock discontinuities of arbitrary strength which lie on a given smooth initial surface with arbitrary geometry. These shock solutions are constructed via a classical iteration scheme. The key step is to obtain the uniform stability for the related linearized equation by calculating the Lopatinski's determinant, which enables us to modify the technique of Majda and establish the local existence of solutions to the pressure gradient system without the structural constraints as for the full Euler system. / In this thesis we study two kinds of multi-dimensional shock phenomena for the compressible fluid dynamics. / Xie Feng. / "December 2005." / Adviser: Zhou Ping Xin. / Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6446. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 71-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343734 |
| Date | January 2005 |
| Contributors | Xie, Feng., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (ii, 80 p. : ill.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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