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  • Controllability and observability for quasilinear hyperbolic systems
  • 點閱:1
  • 並列題名:擬線性雙曲系統的能控性與能觀性
  • 作者: Tatsien Li
  • 出版社:American Institute of Mathematical Sciences Higher Education Press
  • 出版年:2010
  • ISBN:9787040241631
  • 格式:PDF,JPG
  • 附註:Includes index
租期14天 今日租書可閱讀至2021-12-19

The controllability and observability are of great importance in both theory and applications. A complete theory has been established for linear hyperbolic systems, in particular, for linear wave equations. There have also been some results for semilinear wave equations. For quasilinear hyperbolic systems that have numerous applications in mechanics, physics and other applied sciences, however, very few results are available even with space dimension one. This monograph is based mainly on the results obtained by the author and his collaborators in recent years. By means of the theory on the semi-global classical solution, a simple and direct constructive method is presented in a systematic way to get both the controllability and observability in the framework of classical solutions for general first order 1-D quasilinear hyperbolic systems with general nonlinear boundary conditions. Corresponding applications are given for 1-D quasilinear wave equations and 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 especially written for those readers who are not familiar with quasilinear hyperbolic systems. This book will be of benefit to scholars and graduate students in applied mathematics and applied sciences. It may be used as a textbook or a main reference for graduate students in corresponding areas.

  • 1 Introduction(第1頁)
    • 1.1 Exact Controllability(第1頁)
    • 1.2 Exact Observability(第8頁)
    • 1.3 “Duality” Between Controllability and Observability(第12頁)
    • 1.4 Exact Boundary Controllability and Exact Boundary Observability for 1-D Quasilinear Wave Equations(第13頁)
    • 1.5 Exact Boundary Controllability and Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals(第14頁)
    • 1.6 Nonautonomous Hyperbolic Systems(第15頁)
    • 1.7 Notes on the One-Sided Exact Boundary Controllability and Observability(第17頁)
  • 2 Semi-Global C1 Solutions for First Order Quasilinear Hyperbolic Systems(第19頁)
    • 2.1 Introduction(第19頁)
    • 2.2 Equivalence of Problem I and Problem II(第21頁)
    • 2.3 Local C1 Solution to the Mixed Initial-Boundary Value Problem(第27頁)
    • 2.4 Semi-Global C1 Solution to the Mixed Initial-Boundary Value Problem(第27頁)
    • 2.5 Remarks(第33頁)
  • 3 Exact Controllability for First Order Quasilinear Hyperbolic Systems(第37頁)
    • 3.1 Introduction and Main Results(第37頁)
    • 3.2 Framework of Resolution(第41頁)
    • 3.3 Two-Sided Control—Proof of Theorem 3.1(第42頁)
    • 3.4 One-Sided Control—Proof of Theorem 3.2(第47頁)
    • 3.5 Two-Sided Control with Less Controls|Proof of Theorem 3.3(第52頁)
    • 3.6 Exact Controllability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues(第57頁)
  • 4 Exact Observability for First Order Quasilinear Hyperbolic Systems(第63頁)
    • 4.1 Introduction and Main Results(第63頁)
    • 4.2 Two-Sided Observation—Proof of Theorem 4.1(第67頁)
    • 4.3 One-Sided Observation—Proof of Theorem 4.2(第70頁)
    • 4.4 Two-Sided Observation with Less Observed Values—Proof of Theorem 4.3(第71頁)
    • 4.5 Exact Observability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues(第73頁)
    • 4.6 “Duality” Between Controllability and Observability for First Order Quasilinear Hyperbolic Systems(第74頁)
  • 5 Exact Boundary Controllability for Quasilinear Wave Equations(第77頁)
    • 5.1 Introduction and Main Results(第77頁)
    • 5.2 Semi-Global C2 Solution for 1-D Quasilinear Wave Equations(第80頁)
    • 5.3 Two-Sided Control|Proof of Theorem 5.1(第83頁)
    • 5.4 One-Sided Control|Proof of Theorem 5.2(第88頁)
    • 5.5 Remarks(第90頁)
  • 6 Exact Boundary Observability for Quasilinear Wave Equations(第93頁)
    • 6.1 Introduction(第93頁)
    • 6.2 Semi-Global C2 Solution for 1-D Quasilinear Wave Equations (Continued)(第94頁)
    • 6.3 Exact Boundary Observability(第97頁)
    • 6.4 “Duality” Between Controllability and Observability for Quasilinear Wave Equations(第101頁)
  • 7 Exact Boundary Controllability of Unsteady Flows in a Tree-Like Network of Open Canals(第103頁)
    • 7.1 Introduction(第103頁)
    • 7.2 Preliminaries(第105頁)
    • 7.3 Exact Boundary Controllability of Unsteady Flows in a Single Open Canal(第107頁)
    • 7.4 Exact Boundary Controllability for Quasilinear Hyperbolic Systems on a Star-Like Network(第112頁)
    • 7.5 Exact Boundary Controllability of Unsteady Flows in a Star-Like Network of Open Canals(第119頁)
    • 7.6 Exact Boundary Controllability of Unsteady Flows in a Tree-Like Network of Open Canals(第123頁)
    • 7.7 Remarks(第127頁)
  • 8 Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals(第129頁)
    • 8.1 Introduction(第129頁)
    • 8.2 Preliminaries(第130頁)
    • 8.3 Exact Boundary Observability of Unsteady Flows in a Single Open Canal(第132頁)
    • 8.4 Exact Boundary Observability of Unsteady Flows in a Star-Like Network of Open Canals(第136頁)
    • 8.5 Exact Boundary Observability of Unsteady Flows in a Tree-Like Network of Open Canals(第148頁)
    • 8.6 “Duality” Between Controllability and Observability in a Tree-Like Network of Open Canals(第154頁)
  • 9 Controllability and Observability for Nonautonomous Hyperbolic Systems(第155頁)
    • 9.1 Introduction(第155頁)
    • 9.2 Two-Sided Control(第156頁)
    • 9.3 One-Sided Control(第161頁)
    • 9.4 Two-Sided Observation(第164頁)
    • 9.5 One-Sided Observation(第165頁)
    • 9.6 Remarks(第167頁)
  • 10 Note on the One-Sided Exact Boundary Controllability for First Order Quasilinear Hyperbolic Systems(第171頁)
    • 10.1 Introduction(第171頁)
    • 10.2 Reduction of the Problem(第174頁)
    • 10.3 Semi-Global C2 Solution to a Class of Second Order Quasilinear Hyperbolic Equations(第177頁)
    • 10.4 One-Sided Exact Boundary Controllability for a Class of Second Order Quasilinear Hyperbolic Equations(第180頁)
  • 11 Note on the One-Sided Exact Boundary Observability for First Order Quasilinear Hyperbolic Systems(第185頁)
    • 11.1 Introduction(第185頁)
    • 11.2 Reduction of the Problem(第188頁)
    • 11.3 Proof of Theorem 11.1(第190頁)
    • 11.4 “Duality” Between Controllability and Observability(第193頁)
  • Appendix A: An Introduction to Quasilinear Hyperbolic Systems(第195頁)
    • A.1 Definition of Quasilinear Hyperbolic System(第195頁)
    • A.2 Characteristic Form of Hyperbolic System(第198頁)
    • A.3 Reducible Quasilinear Hyperbolic System. Riemann Invariants(第199頁)
    • A.4 Blow-Up Phenomenon(第201頁)
    • A.5 Cauchy Problem(第202頁)
    • A.6 Mixed Initial-Boundary Value Problem(第203頁)
    • A.7 Decomposition of Waves(第205頁)
  • References(第211頁)
  • Index(第217頁)
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租期14天
今日租書可閱讀至2021-12-19
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