LEADER 06093nam 22006255 450 001 9910360849803321 005 20200630022129.0 010 $a3-030-32849-X 024 7 $a10.1007/978-3-030-32849-8 035 $a(CKB)4100000009939740 035 $a(DE-He213)978-3-030-32849-8 035 $a(MiAaPQ)EBC5989088 035 $a(PPN)242818668 035 $a(EXLCZ)994100000009939740 100 $a20191202d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBoundary Synchronization for Hyperbolic Systems$b[electronic resource] /$fby Tatsien Li, Bopeng Rao 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (X, 333 p. 2 illus., 1 illus. in color.) 225 1 $aPNLDE Subseries in Control ;$v94 311 $a3-030-32848-1 327 $aIntroduction 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. 330 $aWithin this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems. 410 0$aPNLDE Subseries in Control ;$v94 606 $aSystem theory 606 $aPartial differential equations 606 $aDifferential equations 606 $aControl engineering 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 615 0$aSystem theory. 615 0$aPartial differential equations. 615 0$aDifferential equations. 615 0$aControl engineering. 615 14$aSystems Theory, Control. 615 24$aPartial Differential Equations. 615 24$aOrdinary Differential Equations. 615 24$aControl and Systems Theory. 676 $a519 700 $aLi$b Tatsien$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755910 702 $aRao$b Bopeng$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910360849803321 996 $aBoundary Synchronization for Hyperbolic Systems$92523259 997 $aUNINA