by Chi-chung Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 45-47). / INTRODUCTION --- p.1 / Chapter CHAPTER 1 --- RADIAL SYMMETRY OF GROUND STATES --- p.7 / Chapter CHAPTER 2 --- EXISTENCE OF A GROUND STATE --- p.14 / Chapter CHAPTER 3 --- UNIQUENESS OF GROUND STATE I --- p.23 / Chapter CHAPTER 4 --- UNIQUENESS OF GROUND STATE II --- p.35 / REFERENCES --- p.45

by Huang Yu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 145-150). / Introduction --- p.1 / Chapter 1 --- Global Attractors of Semigroups --- p.9 / Introduction --- p.9 / Chapter 1.1 --- Basic Notions --- p.9 / Chapter 1.2 --- Semigroup of Class K --- p.11 / Chapter 1.3 --- Semigroup of Class AK --- p.15 / Chapter 1.4 --- Hausdorff and Fractal Dimensions of Attractors --- p.19 / Chapter 1.4.1 --- Hausdorff and Fractal dimensions --- p.20 / Chapter 1.4.2 --- The Dimensions of Invariant Sets --- p.22 / Chapter 1.4.3 --- An Application to Evolution Equations --- p.35 / Notes --- p.39 / Chapter 2 --- Invariant Manifolds and Inertial Manifolds --- p.40 / Introduction --- p.40 / Chapter 2.1 --- Preliminary --- p.41 / Chapter 2.1.1 --- Notions --- p.41 / Chapter 2.1.2 --- Nemytskii Operator --- p.43 / Chapter 2.1.3 --- Contractions on Embedded Banach Spaces --- p.47 / Chapter 2.2 --- Linear and Nonlinear Integral Equations --- p.49 / Chapter 2.3 --- Invariant Manifolds --- p.55 / Chapter 2.4 --- Inertial Manifolds --- p.59 / Notes --- p.63 / Chapter 3 --- Semilinear Parabolic Variational Inequalities --- p.64 / Introduction --- p.64 / Chapter 3.1 --- Existence Results --- p.66 / Chapter 3.2 --- The Existence of Global Attractors --- p.69 / Chapter 3.3 --- The Weakly Approximating Inertial Manifolds --- p.76 / Chapter 3.4 --- An Application: The Obstacle Problem --- p.87 / Chapter 4 --- Semilinear Wave Equations with Damping and Critical Expo- nent --- p.91 / Introduction --- p.91 / Chapter 4.1 --- Existence Results --- p.93 / Chapter 4.2 --- The Global Attractor for the Problem --- p.96 / Chapter 4.2.1 --- A Proposition on Uniform Decay --- p.98 / Chapter 4.2.2 --- Compactness of the Trajectories of (4.2.7) --- p.102 / Chapter 4.3 --- A Particular Case-Linear Damping --- p.105 / Chapter 4.4 --- Estimate of the Dimensions of the Global Attractor --- p.111 / Chapter 4.4.1 --- The Linearized Equation --- p.114 / Chapter 4.4.2 --- The Hausdorff and Fractal Dimensions of the Attractor --- p.117 / Chapter 5 --- Partially Dissipative Evolution Equations --- p.123 / Introduction --- p.123 / Chapter 5.1 --- Basic Notions --- p.124 / Chapter 5.2 --- Semilinear Parabolic Equations and Systems --- p.128 / Chapter 5.3 --- Semilinera Hyperbolic Equation with Damping --- p.136 / Reference --- p.145

Chu Shun Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.8 / Chapter 2 --- Singular Integrals --- p.15 / Chapter 2.1 --- Marcinkiewicz Integral --- p.15 / Chapter 2.2 --- Decomposition in cubes of open sets in Rn --- p.17 / Chapter 2.3 --- Interpolation Theorem for Lp --- p.18 / Chapter 2.4 --- Singular Integrals on homogeneous of degree 0 --- p.25 / Chapter 3 --- Solutions to the Euler Equations --- p.36 / Chapter 3.1 --- Existence and Uniqueness of smooth solutions for Euler Equations --- p.36 / Chapter 3.2 --- Rate of Convergence and Decay in Time --- p.43 / Chapter 3.2.1 --- Rate of Convergence --- p.43 / Chapter 3.2.2 --- Lp Decay for Solutions of the Navier-Stokes Equations --- p.46 / Chapter 3.3 --- Weak Solution to the Euler Equations --- p.48 / Chapter 3.3.1 --- Weak Solution to the Velocity Formulation --- p.49 / Chapter 3.3.2 --- Weak Solution to the Vorticity Formulation --- p.52 / Bibliography --- p.63

by Ho Wing Kin. / Thesis submitted in: July 1997. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 89-92). / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- The Euler-Lagrange Equation for Capillary Surfaces --- p.6 / Chapter 1.2 --- The Capillary Tube --- p.12 / Chapter 2 --- Comparison Principles --- p.16 / Chapter 2.1 --- The General Comparison Principle --- p.16 / Chapter 2.2 --- Applications --- p.24 / Chapter 3 --- Existence Criteria --- p.30 / Chapter 3.1 --- Necessary Conditions --- p.31 / Chapter 3.2 --- Sufficient Conditions --- p.35 / Chapter 4 --- Uniqueness --- p.53 / Chapter 4.1 --- General Bounded Domains Case --- p.53 / Chapter 4.2 --- Infinite Strip Case --- p.56 / Chapter 5 --- Gradient Estimate of Surfaces of Constant Mean Curvature --- p.66 / Chapter 5.1 --- The Gradient Estimate --- p.67 / Chapter 5.2 --- Behavior as R→ 1 --- p.70 / Chapter 5.3 --- Existence of the Comparison Surfaces --- p.76 / Chapter 5.4 --- Ro is Best Possible --- p.82 / Appendix Mean Curvature --- p.85

Keung Yee Lo. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 109-111). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Inverse problems and Parameter Identification --- p.1 / Chapter 1.2 --- Examples in inverse problems --- p.2 / Chapter 1.3 --- Applications in parameter identifications --- p.5 / Chapter 1.4 --- Difficulties arising in inverse problems --- p.7 / Chapter 2 --- Identifying Parameters in Parabolic Systems --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.2 --- An averaging-terminal status formulation and existence of its solutions --- p.12 / Chapter 2.3 --- Optimization approach and its convergence --- p.17 / Chapter 2.4 --- Unconstrained minimization problems --- p.26 / Chapter 2.5 --- Armijo algorithm --- p.28 / Chapter 2.6 --- Numerical experiments --- p.32 / Chapter 2.6.1 --- Convergence of the minimization problem --- p.40 / Chapter 2.7 --- Noisy data --- p.59 / Chapter 3 --- Identifying Parameters in Elliptic Systems --- p.68 / Chapter 3.1 --- Augmented Lagrangian Method --- p.68 / Chapter 3.2 --- The discrete saddle-point problem --- p.70 / Chapter 3.3 --- An Uzawa algorithm --- p.71 / Chapter 3.4 --- Formulation of the algorithm --- p.73 / Chapter 3.5 --- Numerical experiments --- p.76 / Chapter 3.6 --- Alternative formulation of the cost functional --- p.90 / Chapter 3.7 --- Iterative GMRES method --- p.102 / Bibliography --- p.109

by Chi-Fai Chan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 53-54). / Abstract also in Chinese. / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter §1.1 --- Polynomial Interpolation --- p.1 / Chapter §1.2 --- Conjugate Gradient Type Methods --- p.6 / Chapter §1.3 --- Outline of the Thesis --- p.10 / Chapter Chapter 2 --- INTEGRAL EQUATIONS --- p.11 / Chapter §2.1 --- Integral Equations --- p.11 / Chapter §2.2 --- Numerical Treatments of Second Kind Integral Equations --- p.15 / Chapter Chapter 3 --- FAST ALGORITHM FOR SECOND KIND INTEGRAL EQUATIONS --- p.20 / Chapter §3.1 --- Introduction --- p.20 / Chapter §3.2 --- The Approximation --- p.24 / Chapter §3.3 --- Error Analysis --- p.35 / Chapter §3.4 --- Numerical Examples --- p.40 / Chapter §3.5 --- Concluding Remarks --- p.51 / References --- p.53

Mak, Tsz Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 33-36). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Wang Yuliang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 70-75). / Abstracts in English and Chinese. / Chapter 1 --- Introduction to Inverse Problems --- p.1 / Chapter 1.1 --- Typical Examples --- p.1 / Chapter 1.2 --- Major Properties --- p.3 / Chapter 1.3 --- Solution Methods --- p.4 / Chapter 1.4 --- Thesis Outline --- p.4 / Chapter 2 --- Review of the Theory --- p.6 / Chapter 2.1 --- Basic Concepts --- p.6 / Chapter 2.1.1 --- Ill-posedness --- p.6 / Chapter 2.1.2 --- Generalized Inverse --- p.7 / Chapter 2.1.3 --- Compact Operators and SVE --- p.8 / Chapter 2.2 --- Regularization Methods --- p.10 / Chapter 2.2.1 --- An Overview --- p.11 / Chapter 2.2.2 --- Convergence Rates --- p.12 / Chapter 2.2.3 --- Parameter Choice Rules --- p.15 / Chapter 2.2.4 --- Classical Regularization Methods --- p.18 / Chapter 3 --- Ill-posedenss of Typical Inverse Problems --- p.23 / Chapter 3.1 --- Integral Equations --- p.24 / Chapter 3.2 --- Inverse Source Problems --- p.26 / Chapter 3.3 --- Parameter Identification --- p.34 / Chapter 3.4 --- Backward Heat Conduction --- p.37 / Chapter 4 --- Error Estimates for Parameter Identification --- p.39 / Chapter 4.1 --- Overview of Numerical Methods --- p.40 / Chapter 4.2 --- Finite Element Spaces and Standard Estimates --- p.43 / Chapter 4.3 --- Output Least-square Methods --- p.43 / Chapter 4.4 --- Equation Error Methods --- p.50 / Chapter 4.5 --- Hybrid Methods --- p.50 / Chapter 5 --- Numerical Experiments --- p.52 / Chapter 5.1 --- Formulate the Linear Systems --- p.53 / Chapter 5.2 --- Test Problems and Observations --- p.55 / Bibliography --- p.70

In this thesis, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d'Alembertian equation. In particular, we prove the solution decays to a linearlized Kerr solution except for the angular mode l=2.

by Li Jingzhi. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 56-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Parameter identification problems --- p.1 / Chapter 1.2 --- Overview of existing numerical methods --- p.2 / Chapter 1.3 --- Outline of the thesis --- p.4 / Chapter 2 --- General Framework --- p.6 / Chapter 2.1 --- Abstract inverse problem --- p.6 / Chapter 2.2 --- Abstract multilevel models --- p.7 / Chapter 2.3 --- Abstract MMC algorithm --- p.9 / Chapter 3 --- Dual Viewpoint and Convergence Condition --- p.15 / Chapter 3.1 --- Dual viewpoint of nonlinear multigrid method --- p.15 / Chapter 3.2 --- Convergence condition of MMC algorithm --- p.16 / Chapter 4 --- Applications of MMC Algorithm for Parameter Identification in Elliptic and Parabolic Systems --- p.20 / Chapter 4.1 --- Notations --- p.20 / Chapter 4.2 --- Parameter identification in elliptic systems I --- p.21 / Chapter 4.3 --- Parameter identification in elliptic systems II --- p.23 / Chapter 4.4 --- Parameter identification in parabolic systems I --- p.24 / Chapter 4.5 --- Parameter identification in parabolic systems II --- p.25 / Chapter 5 --- Numerical Experiments --- p.27 / Chapter 5.1 --- Test problems --- p.27 / Chapter 5.2 --- Smoothing property of gradient methods --- p.28 / Chapter 5.3 --- Numerical examples --- p.29 / Chapter 6 --- Conclusion Remarks --- p.55 / Bibliography --- p.56