Department of Cultural and Religious Studies, The Chinese University of Hong Kong
Abstract
Guo Bao Zhu.Thesis (Ph.D.)--Chinese University of Hong Kong.Includes bibliographical references.Abstract --- p.1Introduction --- p.3Chapter Chapter 1. --- Semigroup for Age-Dependent Population Equations with Time DelayChapter 1.1 --- Introduction --- p.13Chapter 1.2 --- Problem Statement and Linear Theory --- p.14Chapter 1.3 --- Spectral Properties of the Infinitesimal Generator --- p.20Chapter 1.4 --- A Nonlinear Semigroup of the Logistic Age-Dependent Model with Delay --- p.26References --- p.34Chapter Chapter 2. --- Global Behaviour of Logistic Model of Age-Dependent Population GrowthChapter 2.1 --- Introduction --- p.35Chapter 2.2 --- Global Behaviour of the Solutions --- p.37Chapter 2.3 --- Oscillatory Properties --- p.47References --- p.51Chapter Chapter 3. --- Semigroups for Age-Size Dependent Population Equations with Spatial DiffusionChapter 3. 1 --- Introduction --- p.52Chapter 3.2 --- Properties of the Infinitesimal Generator --- p.54Chapter 3.3 --- Properties of the Semigroup --- p.59Chapter 3.4 --- Dynamics with Age-Size Structures --- p.61Chapter 3.5 --- Logistic Model with Diffusion --- p.66References --- p.70Chapter Chapter 4. --- Semi-Discrete Population Equations with Time DelayChapter 4. 1 --- Introduction --- p.72Chapter 4.2 --- Linear Semi-Discrete Model with Time Delay --- p.74Chapter 4.3 --- Nonlinear Semi-Discrete Model with Time Delay --- p.88References --- p.98Chapter Chapter 5. --- A Finite Difference Scheme for the Equations of Population DynamicsChapter 5.1 --- Introduction --- p.99Chapter 5.2 --- The Discrete System --- p.102Chapter 5.3 --- The Main Results --- p.107Chapter 5.4 --- A Finite Difference Scheme for Logistic Population Model --- p.113Chapter 5.5 --- Numerical Simulation --- p.116References --- p.119Chapter Chapter 6. --- Optimal Birth Control Policies IChapter 6. 1 --- Introduction --- p.120Chapter 6.2 --- Fixed Horizon and Free Point Problem --- p.120Chapter 6.3 --- Time Optimal Control Problem --- p.129Chapter 6.4 --- Infinite Horizon Problem --- p.130Chapter 6.5 --- Results of the Nonlinear System with Logistic Term --- p.143Reference --- p.148Chapter Chapter 7. --- Optimal Birth Control Policies IIChapter 7. 1 --- Free Final Time Problems --- p.149Chapter 7.2 --- Systems with Phase Constraints --- p.160Chapter 7.3 --- Mini-Max Problems --- p.166References --- p.168Chapter Chapter 8. --- Perato Optimal Birth Control PoliciesChapter 8.1 --- Introduction --- p.169Chapter 8.2 --- The Duboviskii-Mi1yutin Theorem --- p.171Chapter 8.3 --- Week Pareto Minimum Principle --- p.172Chapter 8.4 --- Problem with Nonsmooth Criteria --- p.175References --- p.181Chapter Chapter 9. --- Overtaking Optimal Control Problems with Infinite HorizonChapter 9. 1 --- Introduction --- p.182Chapter 9.2 --- Problem Statement --- p.183Chapter 9.3 --- The Turnpike Property --- p.190Chapter 9.4 --- Existence of Overtaking Optimal Solutions --- p.196References --- p.198Chapter Chapter 10. --- Viable Control in Logistic Populatiuon ModelChapter 10. 1 --- Introduction --- p.199Chapter 10. 2 --- Viable Control --- p.200Chapter 10.3 --- Minimum Time Problem --- p.205References --- p.208Author's Publications During the Candidature --- p.20
