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Boundary synchronization for hyperbo...

Li, Tatsien.

Boundary synchronization for hyperbolic systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Boundary synchronization for hyperbolic systemsby Tatsien Li, Bopeng Rao.
Author:	Li, Tatsien.
other author:	Rao, Bopeng.
Published:	Cham :Springer International Publishing :2019.
Description:	x, 333 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Boundary value problems.
Online resource:	https://doi.org/10.1007/978-3-030-32849-8
ISBN:	9783030328498$q(electronic bk.)

Boundary synchronization for hyperbolic systems
Li, Tatsien.

Boundary synchronization for hyperbolic systems[electronic resource] /by Tatsien Li, Bopeng Rao. - Cham :Springer International Publishing :2019. - x, 333 p. :ill., digital ;24 cm. - Progress in nonlinear differential equations and their applications ;v.94. - Progress in nonlinear differential equations and their applications ;v.83..

Introduction and Overview -- Preliminaries -- Part 1: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Exact Boundary Synchronization -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization and non-exact boundary synchronization -- Exactly synchronizable states -- Exact boundary synchronization by groups -- Exactly synchronizable states by p-groups -- Part 2: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Approximate Boundary Synchronization -- Approximate boundary synchronization -- Approximate boundary synchronization by p-groups -- Induced approximate boundary synchronization -- Part 3: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Exact Boundary Synchronization -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization and non-exactly boundary synchronization -- Exact boundary synchronization by p-groups -- Determination of exactly synchronizable states by p-groups -- Part 4: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Approximate Boundary Synchronization -- Approximate boundary null controllability -- Approximate boundary synchronization -- Approximate Boundary Synchronization by p-groups -- Part 5: Synchronization for a Coupled System of Wave Equations with Coupled Robin Boundary Controls: Exact Boundary Synchronization -- Preliminaries on problem (III) and (III0) -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization -- Determination of exactly synchronizable states -- Exact boundary synchronization by p-groups -- Necessity of the conditions of Cp-compatibility -- Determination of exactly synchronizable states by p-groups -- Part 6. Synchronization for a Coupled System of Wave Equations with Coupled Boundary Controls: Approximate Boundary Synchronization -- Some algebraic lemmas -- Approximate boundary null controllability -- Unique continuation for Robin problem -- Approximate boundary synchronization -- Approximate boundary synchronization by p-groups -- Approximately synchronizable states by p-groups -- Closing remarks.

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.

ISBN: 9783030328498$q(electronic bk.)

Standard No.: 10.1007/978-3-030-32849-8doiSubjects--Topical Terms:

206979
Boundary value problems.

LC Class. No.: QA379 / .L5 2019

Dewey Class. No.: 515.3535

Boundary synchronization for hyperbolic systems
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490 1 $a Progress in nonlinear differential equations and their applications ; $v v.94
505 0 $a Introduction and Overview -- Preliminaries -- Part 1: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Exact Boundary Synchronization -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization and non-exact boundary synchronization -- Exactly synchronizable states -- Exact boundary synchronization by groups -- Exactly synchronizable states by p-groups -- Part 2: Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls: Approximate Boundary Synchronization -- Approximate boundary synchronization -- Approximate boundary synchronization by p-groups -- Induced approximate boundary synchronization -- Part 3: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Exact Boundary Synchronization -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization and non-exactly boundary synchronization -- Exact boundary synchronization by p-groups -- Determination of exactly synchronizable states by p-groups -- Part 4: Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls: Approximate Boundary Synchronization -- Approximate boundary null controllability -- Approximate boundary synchronization -- Approximate Boundary Synchronization by p-groups -- Part 5: Synchronization for a Coupled System of Wave Equations with Coupled Robin Boundary Controls: Exact Boundary Synchronization -- Preliminaries on problem (III) and (III0) -- Exact boundary controllability and non-exact boundary controllability -- Exact boundary synchronization -- Determination of exactly synchronizable states -- Exact boundary synchronization by p-groups -- Necessity of the conditions of Cp-compatibility -- Determination of exactly synchronizable states by p-groups -- Part 6. Synchronization for a Coupled System of Wave Equations with Coupled Boundary Controls: Approximate Boundary Synchronization -- Some algebraic lemmas -- Approximate boundary null controllability -- Unique continuation for Robin problem -- Approximate boundary synchronization -- Approximate boundary synchronization by p-groups -- Approximately synchronizable states by p-groups -- Closing remarks.
520 $a 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.
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