Chen, Chao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 43-46). / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.7 / Chapter 3 --- The mathematical formulation of the problem and main results --- p.11 / Chapter 4 --- Reformulation of the problem --- p.17 / Chapter 5 --- Proof of the main theorems --- p.23 / Chapter 5.1 --- Proof of uniqueness --- p.23 / Chapter 5.2 --- Proof of non-existence --- p.31 / Chapter 6 --- Work in future --- p.40 / Chapter 7 --- Appendix --- p.41 / Bibliography --- p.43

Shocked porous granular material experiences pressure dependent compaction. D. John Pastine introduced a model in which the degree of compaction is dependent on the pressure induced by the shock wave, the shear strength of the material, and the distribution of void sizes. In the past, the model could only be approximated. Using computational techniques and higher speed computers, the response of this model to void size distributions may be displayed to a high degree of precision. / Graduation date: 1996

First, we investigate the steady Euler flows through a general 3-D axially symmetric infinitely long nozzles without irrotationality. Global existence and uniqueness of subsonic solution are established, when the variation of Bernoulli's function in the upstream is sufficiently small and mass flux has an upper critical value. / Second, we concerns the following transonic shock phenomena in a class of de Laval nozzles with porous medium posed by Courant-Friedrichs: Given a appropriately large receiver pressure pr, if the upstream flow is still supersonic behind the throat of the nozzle, then at a certain place in the diverging part of the nozzle a shock front intervenes and the gas is compressed and slowed down to subsonic speed. The position and the strength of the shock front are automatically adjusted so that the end pressure at the exit becomes pr. We investigate this problem for the full Euler equations, the stability of the transonic shock is proved when the upstream supersonic flow is a small steady perturbation of the uniform supersonic flow and the corresponding pressure at the exit has a small perturbation. / Duan, Ben. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 125-137). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Weng, Shangkun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 73-78). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Existence and Uniqueness results of transonic shock solution to full Euler system in a large variable nozzle --- p.11 / Chapter 2.1 --- The mathematical description of the transonic shock problem and main results --- p.11 / Chapter 2.2 --- The reformulation on problem (2.1.1) with (2.1.5)-(2.1.9) --- p.18 / Chapter 2.3 --- An Iteration Scheme --- p.30 / Chapter 2.4 --- A priori estimates and proofs of Theorem 2.2.1 and Theorem 2.1.1 --- p.39 / Chapter 3 --- A monotonic theorem on the shock position with respect to the exit pressure --- p.50 / Chapter 4 --- Discussions and Future work --- p.64 / Chapter 5 --- Appendix --- p.66 / Chapter 5.1 --- Appendix A: Background solution --- p.66 / Chapter 5.2 --- Appendix B: An outline of the proof of Theorem 2.1.2 --- p.67

Fu Sau-chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 68-71). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Explosion and Implosion Problems --- p.1 / Chapter 1.2 --- Background of the Development of Numerical Schemes --- p.2 / Chapter 1.3 --- Organization of the Thesis --- p.5 / Chapter 2 --- Governing Equations and Numerical Schemes --- p.6 / Chapter 2.1 --- Governing Equations --- p.6 / Chapter 2.2 --- Numerical Schemes --- p.8 / Chapter 2.2.1 --- Splitting Scheme for Partial Differential Equations with Source Terms --- p.8 / Chapter 2.2.2 --- Boundary Conditions --- p.9 / Chapter 2.2.3 --- "Numerical Solvers for the ODEs - The Second-Order, Two-Stage Runge-Kutta Method" --- p.10 / Chapter 2.2.4 --- Numerical Solvers for the Pure Advection Hyperbolic Problem - The Second-Order Relaxed Scheme --- p.11 / Chapter 3 --- Numerical Results --- p.29 / Chapter 3.1 --- Spherical Explosion Problem --- p.30 / Chapter 3.1.1 --- Physical Description --- p.32 / Chapter 3.1.2 --- Comparison with Previous Analytical and Experimental Results --- p.33 / Chapter 3.2 --- Cylindrical Explosion Problem --- p.46 / Chapter 3.2.1 --- Physical Description --- p.46 / Chapter 3.2.2 --- Two-Dimensional Model --- p.49 / Chapter 3.3 --- Spherical Implosion Problem --- p.52 / Chapter 3.3.1 --- Physical Description --- p.52 / Chapter 3.4 --- Cylindrical Implosion Problem --- p.53 / Chapter 3.4.1 --- Physical Description --- p.53 / Chapter 3.4.2 --- Two-Dimensional Model --- p.53 / Chapter 4 --- Conclusion --- p.65 / Bibliography --- p.68