| 摘要 | 第4-5页 |
| Abstract | 第5页 |
| Chapter 1 Introduction | 第8-9页 |
| Chapter 2 The Riemann problem of the homogeneous shallow water equations | 第9-15页 |
| 2.1 The homogenous shallow water equations | 第9页 |
| 2.2 The Riemann solver | 第9-15页 |
| Chapter 3 The Riemann problem for the shallow water equations with a bottom step | 第15-32页 |
| 3.1 The shallow water equations with bottom topography | 第15-16页 |
| 3.2 The exact solution | 第16-32页 |
| 3.2.1 Solutions containing R~1 and S~2 | 第16-22页 |
| 3.2.2 Solutions containing S~1 and S~2 | 第22-26页 |
| 3.2.3 Solutions containing S~1 and R~2 | 第26-30页 |
| 3.2.4 Solutions containing R~1 and R~2 | 第30-32页 |
| Chapter 4 Conclusions | 第32-33页 |
| Bibliography | 第33-35页 |
| ACKNOWLEDGEMENT | 第35页 |
