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Some studies on non-strictly hyperbolic conservation laws.

Wong Tak Kwong. / Thesis submitted in: August 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 67-72). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- Basic Notations --- p.7 / Chapter 1.2 --- Riemann Problems --- p.10 / Chapter 1.3 --- Elementary Waves --- p.10 / Chapter 1.3.1 --- Rarefaction Waves --- p.11 / Chapter 1.3.2 --- Shock Waves --- p.11 / Chapter 1.3.3 --- Composite Waves --- p.13 / Chapter 1.4 --- Remarks --- p.14 / Chapter 2 --- Non-strictly Hyperbolic Conservation Laws --- p.16 / Chapter 2.1 --- Systems with Isolated Umbilic Degeneracy --- p.16 / Chapter 2.1.1 --- Mathematical Motivations --- p.17 / Chapter 2.2 --- Complex Burgers' Equation --- p.21 / Chapter 2.2.1 --- Introduction --- p.21 / Chapter 2.2.2 --- Basic Properties --- p.22 / Chapter 2.2.3 --- Riemann Solutions --- p.24 / Chapter 2.2.4 --- Under-Compressive Shocks --- p.31 / Chapter 3 --- Relaxation Approximation --- p.34 / Chapter 3.1 --- Basic Ideas of the Relaxation Approximation --- p.34 / Chapter 3.1.1 --- General Settings --- p.35 / Chapter 3.1.2 --- Subcharacteristic Condition --- p.36 / Chapter 3.2 --- Relaxation of Scalar Conservation Laws --- p.39 / Chapter 3.2.1 --- Perturbation Problems --- p.39 / Chapter 3.3 --- Jin-Xin Relaxation Systems --- p.42 / Chapter 3.3.1 --- Basic Ideas of the Jin-Xin Systems --- p.42 / Chapter 3.4 --- Zero-Relaxation Limit --- p.45 / Chapter 3.4.1 --- 2x2 Hyperbolic Relaxation Systems --- p.45 / Chapter 3.4.2 --- Jin-Xin Relaxation Systems --- p.48 / Chapter 4 --- Jin-Xin Relaxation Limit for the Complex Burgers' Equations --- p.51 / Chapter 4.1 --- Jin-Xin Relaxation Limit for the UCUI Solutions --- p.52 / Chapter 4.1.1 --- Main Statements --- p.52 / Chapter 4.1.2 --- Analysis on UCUI Solution --- p.53 / Chapter 4.1.3 --- Shock Profiles --- p.56 / Chapter 4.1.4 --- Re-scaled Relaxation System --- p.60 / Chapter 4.1.5 --- Proof of Theorem 4.1.1.3 --- p.63 / Bibliography --- p.67

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_325187
Date January 2005
ContributorsWong, Tak Kwong., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, 72 leaves : ill. ; 30 cm.
RightsUse 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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