本专著基于作者和他的研究团队在近些年的研究成果，较为系统地介绍了利用半全局经典解的理论，用一种简单并直接的构造方法，针对具有通常非线性边界条件的一阶一维拟线性双曲型方程，在经典解的框架下的得到能控性及能观性，同时书中还给出了针对一维拟线性波动方程的有关应用，以及对开放槽树形网络不稳定流的应用。
Introduction
1.1 Exact Controllability
1.2 Exact Observability
1.3 "Duality" Between Controllability and Observability
1.4 Exact Boundary Controllability and Exact Boundary Observability for 1-D Quasilinear Wave Equations
1.5 Exact Boundary Controllability and Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals
1.6 Nonautonomous Hyperbolic Systems
1.7 Notes on the One-Sided Exact Boundary Controllability and Observability
2 Semi-Global C1 Solutions for First Order Quasilinear Hyperbolic Systems
2.1 Introduction
2.2 Equivalence of Problem I and Problem II
2.3 Local C1 Solution to the Mixed Initial-Boundary Value Problem
2.4 Semi-Global C1 Solution to the Mixed Initial-Boundary Value Problem
2.5 Remarks
3 Exact Controllability for First Order Quasilinear Hyperbolic Systems
3.1 Introduction and Main Results
3.2 Framework of Resolution
3.3 Two-Sided Control——Proof of Theorem 3.1
3.4 One-Sided Control——Proof of Theorem 3.2
3.5 Two-Sided Control with Less Controls——Proof of Theorem 3.3.
3.6 Exact Controllability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues
4 Exact Observability for First Order Quasilinear Hyperbolic Systems
4.1 Introduction and Main Results
4.2 Two-Sided Observation——Proof of Theorem 4.1
4.3 One-Sided Observation——Proof of Theorem 4.2
4.4 Two-Sided Observation with Less Observed Values——Proof of Theorem 4.3
4.5 Exact Observability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues
4.6 "Duality" Between Controllability and Observability for First Order Quasilinear Hyperbolic Systems
5 Exact Boundary Controllability for Quasilinear Wave Equations
5.1 Introduction and Main Results
5.2 Semi-Global C2 Solution for 1-D Quasilinear Wave Equations
5.3 Two-Sided Control——Proof of Theorem 5.1
5.4 One-Sided Control——Proof of Theorem 5.2
5.5 Remarks
6 Exact Boundary Observability for Quasilinear Wave Equations
6.1 Introduction
6.2 Semi-Global C2 Solution for 1-D Quasilinear Wave Equations （Continued）
6.3 Exact Boundary Observability
6.4 "Duality" Between Controllability and Observability for Quasilinear Wave Equations
7 Exact Boundary Controllability of Unsteady Flows in a Tree-Like Network of Open Canals
7.1 Introduction
7.2 Preliminaries
7.3 Exact Boundary Controllability of Unsteady Flows in a Single Open Canal
7.4 Exact Boundary Controllability for Quasilinear Hyperbolic Systems on a Star-Like Network
7.5 Exact Boundary Controllability of Unsteady Flows in a Star-Like Network of Open Canals
7.6 Exact Boundary Controllability of Unsteady Flows in a Tree-Like Network of Open Canals
7.7 Remarks
8 Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals
8.1 Introduction
8.2 Preliminaries
8.3 Exact Boundary Observability of Unsteady Flows in a Single Open Canal
8.4 Exact Boundary Observability of Unsteady Flows in a
Star-Like Network of Open Canals 8.5 Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals
8.6 "Duality" Between Controllability and Observability in a Tree-Like Network of Open Canals
9 Controllability and Observability for Nonautonomous Hyperbolic Systems
9.1 Introduction
9.2 Two-Sided Control
9.3 One-Sided Control
9.4 Two-Sided Observation
9.5 One-Sided Observation
9.6 Remarks
10 Note on the One-Sided Exact Boundary Controllability for First Order Quasilinear Hyperbolic Systems
10.1 Introduction
10.2 Reduction of the Problem
10.3 Semi-Global C2 Solution to a Class of Second Order Quasilinear Hyperbolic Equations
10.4 One-Sided Exact Boundary Controllability for a Class of
Second Order Quasilinear Hyperbolic Equations
11 Note on the One-Sided Exact Boundary Observability for First Order Quasilinear Hyperbolic Systems
11.1 Introduction
11.2 Reduction of the Problem
11.3 Proof of Theorem 11.1
11.4 "Duality" Between Controllability and Observability
Appendix A： An Introduction to Quasilinear Hyperbolic Systems
A.1 Definition of Quasilinear Hyperbolic System
A.2 Characteristic Form of Hyperbolic System
A.3 Reducible Quasilinear Hyperbolic System. Riemann Invariants
A.4 Blow-Up Phenomenon
A.5 Cauchy Problem
A.6 Mixed Initial-Boundary Value Problem
A.7 Decomposition of Waves
References
Index
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