擬線性雙曲系統(tǒng)的能控性與能觀性

前言

The controllability and observability are of great importance in both theoryand applications. A complete theory has been established for linear hyperbolicsystems, in particular, for linear wave equations. There have also been someresults for semilinear wave equations. For quasilinear hyperbolic systems, how-ever, very few results have been published even in the one-space-dimensional（l-D） case.In this monograph based mainly on the results obtained by the authorand his collaborators in recent years, by means of the theory on the semi-global classical 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 quasilinear hyper-bolic systems with general nonlinear boundary conditions, and correspondingapplications are given for 1-D quasilinear wave equations and for unsteadyflows in a tree-like network of open canals, respectively. This will be of bene-fit to scholars and graduate students in applied mathematics and in appliedsciences.The Appendix given at the end of this monograph is specially written forthose readers who are not familiar with quasilinear hyperbolic systems.I would like to take this opportunity to express my sincere thanks tothe late professor J.-L. Lions, who initiated and brought me into the areaof control theory, for his encouragement and guidance. My special thanksare due to Bopeng Rao, Binyu Zhang, Yi Jin, Lixin Yu, Zhiqiang Wang andQilong Gu for their kind cooperation in the course of research on this subject,supported by the National Basic Research Program of China （973 Program）（2007CB814800）. Finally, I am also indebted to Ms. Chunlian Zhou for herpatient and efficient work in editing this book.

內(nèi)容概要

　　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.

書籍目錄

Introduction1.1 Exact Controllability1.2 Exact Observability1.3 "Duality" Between Controllability and Observability1.4 Exact Boundary Controllability and Exact Boundary Observability for 1-D Quasilinear Wave Equations1.5 Exact Boundary Controllability and Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals1.6 Nonautonomous Hyperbolic Systems1.7 Notes on the One-Sided Exact Boundary Controllability and Observability2 Semi-Global C1 Solutions for First Order Quasilinear Hyperbolic Systems2.1 Introduction2.2 Equivalence of Problem I and Problem II2.3 Local C1 Solution to the Mixed Initial-Boundary Value Problem2.4 Semi-Global C1 Solution to the Mixed Initial-Boundary Value Problem2.5 Remarks3 Exact Controllability for First Order Quasilinear Hyperbolic Systems3.1 Introduction and Main Results3.2 Framework of Resolution3.3 Two-Sided Control——Proof of Theorem 3.13.4 One-Sided Control——Proof of Theorem 3.23.5 Two-Sided Control with Less Controls——Proof of Theorem 3.3.3.6 Exact Controllability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues4 Exact Observability for First Order Quasilinear Hyperbolic Systems4.1 Introduction and Main Results4.2 Two-Sided Observation——Proof of Theorem 4.14.3 One-Sided Observation——Proof of Theorem 4.24.4 Two-Sided Observation with Less Observed Values——Proof of Theorem 4.34.5 Exact Observability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues4.6 "Duality" Between Controllability and Observability for First Order Quasilinear Hyperbolic Systems5 Exact Boundary Controllability for Quasilinear Wave Equations5.1 Introduction and Main Results5.2 Semi-Global C2 Solution for 1-D Quasilinear Wave Equations5.3 Two-Sided Control——Proof of Theorem 5.15.4 One-Sided Control——Proof of Theorem 5.25.5 Remarks6 Exact Boundary Observability for Quasilinear Wave Equations6.1 Introduction6.2 Semi-Global C2 Solution for 1-D Quasilinear Wave Equations （Continued）6.3 Exact Boundary Observability6.4 "Duality" Between Controllability and Observability for Quasilinear Wave Equations7 Exact Boundary Controllability of Unsteady Flows in a Tree-Like Network of Open Canals7.1 Introduction7.2 Preliminaries7.3 Exact Boundary Controllability of Unsteady Flows in a Single Open Canal7.4 Exact Boundary Controllability for Quasilinear Hyperbolic Systems on a Star-Like Network7.5 Exact Boundary Controllability of Unsteady Flows in a Star-Like Network of Open Canals7.6 Exact Boundary Controllability of Unsteady Flows in a Tree-Like Network of Open Canals7.7 Remarks 8 Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals8.1 Introduction8.2 Preliminaries8.3 Exact Boundary Observability of Unsteady Flows in a Single Open Canal8.4 Exact Boundary Observability of Unsteady Flows in aStar-Like Network of Open Canals 8.5 Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals8.6 "Duality" Between Controllability and Observability in a Tree-Like Network of Open Canals9 Controllability and Observability for Nonautonomous Hyperbolic Systems9.1 Introduction9.2 Two-Sided Control9.3 One-Sided Control9.4 Two-Sided Observation9.5 One-Sided Observation9.6 Remarks10 Note on the One-Sided Exact Boundary Controllability for First Order Quasilinear Hyperbolic Systems10.1 Introduction10.2 Reduction of the Problem10.3 Semi-Global C2 Solution to a Class of Second Order Quasilinear Hyperbolic Equations10.4 One-Sided Exact Boundary Controllability for a Class ofSecond Order Quasilinear Hyperbolic Equations11 Note on the One-Sided Exact Boundary Observability for First Order Quasilinear Hyperbolic Systems11.1 Introduction11.2 Reduction of the Problem11.3 Proof of Theorem 11.111.4 "Duality" Between Controllability and ObservabilityAppendix A: An Introduction to Quasilinear Hyperbolic SystemsA.1 Definition of Quasilinear Hyperbolic SystemA.2 Characteristic Form of Hyperbolic SystemA.3 Reducible Quasilinear Hyperbolic System. Riemann InvariantsA.4 Blow-Up PhenomenonA.5 Cauchy ProblemA.6 Mixed Initial-Boundary Value ProblemA.7 Decomposition of WavesReferencesIndex

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