| Abstract | 第8页 |
| 摘要 | 第9-10页 |
| Chapter 1 Background and Preliminaries | 第10-18页 |
| Chapter 2 Nonlinear Instability for a Volume-Filling ChemotaxisModel with Bistable Source Term | 第18-37页 |
| 2.1 Introduction | 第18-21页 |
| 2.2 Stability of positive equilibrium point of (2.1.2) without chemotaxis | 第21-22页 |
| 2.3 Growing modes in the system (2.1.1) | 第22-26页 |
| 2.4 Bootstrap Lemma | 第26-31页 |
| 2.5 Nonlinear instability and pattern formation | 第31-37页 |
| Chapter 3 Asymptotic Stability of Constant Equilibrium Point inKeller-Segel Chemotaxis Model with Bistable Source Term | 第37-60页 |
| 3.1 Introduction | 第37-38页 |
| 3.2 Preliminaries | 第38-43页 |
| 3.3 L∞estimate of u. Global existence | 第43-45页 |
| 3.4 Bounds in L~p(?) for △V and A~γU for γ <1/2 | 第45-50页 |
| 3.5 A pointwise estimate for △v | 第50-52页 |
| 3.6 Refined pointwise inequalities for u | 第52-53页 |
| 3.7 Exponential decay. Proof of main result | 第53-60页 |
| Chapter 4 Asymptotic Stability of Constant Equilibrium Point in aVolume-Filling Chemotaxis Model with Bistable Source Term | 第60-83页 |
| 4.1 Introduction | 第60-61页 |
| 4.2 Preliminaries | 第61-66页 |
| 4.3 An explicit bounded for u via comparison. Global existence | 第66-68页 |
| 4.4 Bounds in L~p(?) for △V and A~γU for γ <1/2 | 第68-73页 |
| 4.5 A pointwise estimate for △v | 第73-75页 |
| 4.6 Refined pointwise inequalities for u | 第75-77页 |
| 4.7 Proof of the main result | 第77-83页 |
| Chapter 5 Global Asymptotic Stability of Positive Equilibrium Pointin a Volume-Filling Chemotaxis Model with Logistic Growth | 第83-102页 |
| 5.1 Introduction | 第83-84页 |
| 5.2 Local existence | 第84-85页 |
| 5.3 L∞? estimate of u. Global existence | 第85-87页 |
| 5.4 Bounds in L~p(?) for △V and A~γU for γ <1/2 | 第87-92页 |
| 5.5 A pointwise estimate for △v | 第92-94页 |
| 5.6 Refined pointwise inequalities for u | 第94-95页 |
| 5.7 Proof of Theorem 5.1.1 | 第95-102页 |
| REFERENCES | 第102-107页 |
| Publications | 第107-108页 |
| Acknowledgement | 第108页 |
