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Boundary Synchronization for Hyperbolic Systems

  • Tatsien Li
  • Bopeng Rao
Book

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 94)

Also part of the PNLDE Subseries in Control book sub series (PNLDE-SC, volume 94)

Table of contents

  1. Front Matter
    Pages i-x
  2. Tatsien Li, Bopeng Rao
    Pages 1-17
  3. Tatsien Li, Bopeng Rao
    Pages 19-30
  4. Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Exact Boundary Synchronization

    1. Front Matter
      Pages 31-31
    2. Tatsien Li, Bopeng Rao
      Pages 49-57
    3. Tatsien Li, Bopeng Rao
      Pages 59-68
    4. Tatsien Li, Bopeng Rao
      Pages 69-78
  5. Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Approximate Boundary Synchronization

    1. Front Matter
      Pages 79-79
    2. Tatsien Li, Bopeng Rao
      Pages 81-103
    3. Tatsien Li, Bopeng Rao
      Pages 105-114
    4. Tatsien Li, Bopeng Rao
      Pages 115-132
    5. Tatsien Li, Bopeng Rao
      Pages 133-151
  6. Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Exact Boundary Synchronization

    1. Front Matter
      Pages 153-153
    2. Tatsien Li, Bopeng Rao
      Pages 179-184
    3. Tatsien Li, Bopeng Rao
      Pages 185-198
  7. Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Approximate Boundary Synchronization

    1. Front Matter
      Pages 199-199
    2. Tatsien Li, Bopeng Rao
      Pages 201-214
    3. Tatsien Li, Bopeng Rao
      Pages 215-222
    4. Tatsien Li, Bopeng Rao
      Pages 223-227
  8. Synchronization for a Coupled System of Wave Equations with Coupled Robin Boundary Controls: Exact Boundary Synchronization

    1. Front Matter
      Pages 229-229
    2. Tatsien Li, Bopeng Rao
      Pages 231-238
    3. Tatsien Li, Bopeng Rao
      Pages 243-246
    4. Tatsien Li, Bopeng Rao
      Pages 247-253
    5. Tatsien Li, Bopeng Rao
      Pages 255-258
    6. Tatsien Li, Bopeng Rao
      Pages 259-266
    7. Tatsien Li, Bopeng Rao
      Pages 267-274
  9. Synchronization for a Coupled System of Wave Equations with Coupled Robin Boundary Controls: Approximate Boundary Synchronization

    1. Front Matter
      Pages 275-275
    2. Tatsien Li, Bopeng Rao
      Pages 277-279
    3. Tatsien Li, Bopeng Rao
      Pages 281-283
    4. Tatsien Li, Bopeng Rao
      Pages 285-295
    5. Tatsien Li, Bopeng Rao
      Pages 297-303
    6. Tatsien Li, Bopeng Rao
      Pages 305-313
    7. Tatsien Li, Bopeng Rao
      Pages 315-319
    8. Tatsien Li, Bopeng Rao
      Pages 321-323
  10. Back Matter
    Pages 325-333

About this book

Introduction

Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations.

Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.

Keywords

Partial Differential Equations Ordinary Differential Equations Synchronization Controllability Boundary Synchronization

Authors and affiliations

  • Tatsien Li
    • 1
  • Bopeng Rao
    • 2
  1. 1.School of Mathematical SciencesFudan UniversityShanghaiChina
  2. 2.Institut de Recherche Mathématique AvancéeUniversité de StrasbourgStrasbourgFrance

Bibliographic information