本專著基于作者和他的研究團(tuán)隊(duì)在近些年的研究成果，較為系統(tǒng)地介紹了利用半全局經(jīng)典解的理論，用一種簡(jiǎn)單并直接的構(gòu)造方法，針對(duì)具有通常非線性邊界條件的一階一維擬線性雙曲型方程，在經(jīng)典解的框架下的得到能控性及能觀性，同時(shí)書中還給出了針對(duì)一維擬線性波動(dòng)方程的有關(guān)應(yīng)用，以及對(duì)開放槽樹形網(wǎng)絡(luò)不穩(wěn)定流的應(yīng)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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