The controllability and observability are of great importance in boththeory and applications. A complete theory has been established for linearhyperbolic systems， in particular， for linear wave equations. There havealso been some results for semilinear wave equations. For quasilinearhyperbolic systems that have numerous applications in mechanics， physicsand other applied sciences， however， very few results are available evenwith space dimension one.
This monograph is based mainly on the results obtained by the author andhis collaborators in recent years. By mea~s of the theory on the semi-globalclassical solution， a simple and direct constructive method is presentedin a systematic way to get both the controllability and observability in theframework of classical solutions for general first order 1-D quasilinearhyperbolic systems with general nonlinear boundary conditions.Corresponding applications are given for 1-D quasilinear wave equationsand for unsteady flows in a tree-like network of open canals， respectively.More than one hundred related references are provided.
This book with 11 chapters is self-contained. An appendix is especiallywritten for those readers who are not familiar with quasilinear hyperbolic systems.
This book will be of benefit to scholars and graduate students in appliedmathematics and applied sciences. It may be used as a textbook or a mainreference for graduate students in corresponding areas.
- Front Matter
- 1 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-GlobalC1 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
- 4.5 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
- 版权
