| 中文摘要 | 第1-8页 |
| Abstract | 第8-14页 |
| Chapter 1 Preliminary | 第14-22页 |
| ·Background and significance | 第14-17页 |
| ·Objectives | 第17-19页 |
| ·Research methodology | 第19-22页 |
| ·Development of a well-posedness method | 第19-20页 |
| ·Development of perturbation methods | 第20-22页 |
| Chapter 2 The Asymptotic Stability of the Cauchy Problem for a Generalized Boussinesq Equation | 第22-34页 |
| ·Introduction | 第22-23页 |
| ·Existence and uniqueness theorem | 第23-29页 |
| ·The asymptotic expression of the global solution | 第29-34页 |
| Chapter 3 The Global Stability of an Initial Boundary Value Problem for the Damped Boussinesq Equation | 第34-48页 |
| ·Introduction | 第34-36页 |
| ·Theorem of existence,uniqueness and asymptotics | 第36-37页 |
| ·Proof of theorem 3.3 | 第37-48页 |
| ·Existence of a solution | 第37-43页 |
| ·Uniqueness of the solution | 第43-45页 |
| ·Long time asymptotics | 第45-48页 |
| Chapter 4 The Stability of Solitary Wave for a Generalized Boussinesq Equation | 第48-60页 |
| ·Introduction | 第48-49页 |
| ·Preliminary | 第49-52页 |
| ·Existence and uniqueness theorem | 第52-56页 |
| ·Stability of solitary waves | 第56-60页 |
| Chapter 5 The Global Solution of a Damped Euler-Bernoulli Equation | 第60-72页 |
| ·Introduction | 第60-61页 |
| ·Preliminary | 第61-64页 |
| ·Theorem of well-posedness | 第64-72页 |
| Chapter 6 The Asymptotic Theory of Global Solutions for Semilinear Wave Equations in Three Space Dimensions | 第72-86页 |
| ·Introduction | 第72-73页 |
| ·The well-posedness | 第73-80页 |
| ·Asymptotic validation of global solutions | 第80-82页 |
| ·Example | 第82-86页 |
| Chapter 7 Conclusions and Future Works | 第86-89页 |
| ·Conclusions | 第86-88页 |
| ·Forthcoming works | 第88-89页 |
| Acknowledgments | 第89-90页 |
| References | 第90-97页 |
| Publications during the Ph.D study | 第97页 |
