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Auteur Tatsien Li |
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Boundary Synchronization for Hyperbolic Systems / Tatsien Li / Bâle (CHE) ; Boston, MA : Birkhäuser (2019)
Titre : Boundary Synchronization for Hyperbolic Systems Type de document : document électronique Auteurs : Tatsien Li, ; Bopeng Rao, ; SpringerLink (Online service) Editeur : Bâle (CHE) ; Boston, MA : Birkhäuser Année de publication : 2019 Collection : Progress in Nonlinear Differential Equations and Their Applications, ISSN 1421-1750 num. 94 Importance : X, 333 p. 2 illus., 1 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-030-32849-8 Langues : Anglais (eng) Tags : System theory Partial differential equations Differential equations Control engineering Systems Theory Control Partial Differential Equations Ordinary Differential Equations Control and Systems Theory Résumé : 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 Note de contenu : 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 Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=148258 Boundary Synchronization for Hyperbolic Systems [document électronique] / Tatsien Li, ; Bopeng Rao, ; SpringerLink (Online service) . - Bâle (CHE) ; Boston, MA : Birkhäuser, 2019 . - X, 333 p. 2 illus., 1 illus. in color : online resource. - (Progress in Nonlinear Differential Equations and Their Applications, ISSN 1421-1750; 94) .
ISBN : 978-3-030-32849-8
Langues : Anglais (eng)
Tags : System theory Partial differential equations Differential equations Control engineering Systems Theory Control Partial Differential Equations Ordinary Differential Equations Control and Systems Theory Résumé : 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 Note de contenu : 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 Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=148258 Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems / Tatsien Li / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2016)
Titre : Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems Type de document : document électronique Auteurs : Tatsien Li ; Ke Wang ; SpringerLink (Online service) ; Qilong Gu Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2016 Collection : SpringerBriefs in Mathematics, ISSN 2191-8198 Importance : IX, 108 p. 27 illus Présentation : online resource ISBN/ISSN/EAN : 978-981-10-2842-7 Langues : Anglais (eng) Tags : Mathematics Partial differential equations System theory Systems Theory Control Partial Differential Equations Résumé : This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyperbolic systems Note de contenu : First Order Quasilinear Hyperbolic Systems -- Quasilinear Wave Equations -- Semi-global Piecewise Classical Solutions on a Tree-like Network -- Exact Boundary Controllability of Nodal Prole for 1-D First Order Quasilinear Hyperbolic Systems -- Exact Boundary Controllability of Nodal Prole for 1-D First Order Quasilinear Hyperbolic Systems on a Tree-like Network -- Exact Boundary Controllability of Nodal Prole for 1-D Quasilinear Wave Equations -- Exact Boundary Controllability of Nodal Prole for 1-D Quasilinear Wave Equations on a Planar Tree-like Network of Strings Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124381 Exact Boundary Controllability of Nodal Profile for Quasilinear Hyperbolic Systems [document électronique] / Tatsien Li ; Ke Wang ; SpringerLink (Online service) ; Qilong Gu . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2016 . - IX, 108 p. 27 illus : online resource. - (SpringerBriefs in Mathematics, ISSN 2191-8198) .
ISBN : 978-981-10-2842-7
Langues : Anglais (eng)
Tags : Mathematics Partial differential equations System theory Systems Theory Control Partial Differential Equations Résumé : This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyperbolic systems Note de contenu : First Order Quasilinear Hyperbolic Systems -- Quasilinear Wave Equations -- Semi-global Piecewise Classical Solutions on a Tree-like Network -- Exact Boundary Controllability of Nodal Prole for 1-D First Order Quasilinear Hyperbolic Systems -- Exact Boundary Controllability of Nodal Prole for 1-D First Order Quasilinear Hyperbolic Systems on a Tree-like Network -- Exact Boundary Controllability of Nodal Prole for 1-D Quasilinear Wave Equations -- Exact Boundary Controllability of Nodal Prole for 1-D Quasilinear Wave Equations on a Planar Tree-like Network of Strings Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=124381 Mathematical Model of Spontaneous Potential Well-Logging and Its Numerical Solutions / Tatsien Li / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2014)
Titre : Mathematical Model of Spontaneous Potential Well-Logging and Its Numerical Solutions Type de document : document électronique Auteurs : Tatsien Li ; Yongji Tan ; SpringerLink (Online service) ; Zhijie Cai ; Wei Chen ; Jingnong Wang Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2014 Collection : SpringerBriefs in Mathematics, ISSN 2191-8198 Importance : VII, 67 p. 28 illus., 14 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-642-41425-1 Langues : Anglais (eng) Tags : Mathematics Physical geography Functional analysis Differential equations Numerical analysis Partial Differential Equations Geophysics Geodesy Numerical Analysis Functional Analysis Résumé : Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axi-symmetric situation the well-posedness of the corresponding mathematical model is proved and three efficient schemes of numerical solution are proposed, supported by a number of numerical examples to meet practical computation needs Note de contenu : Preface -- Modeling -- Properties of solutions -- Limiting behavior -- Techniques of solution -- Numerical simulation -- Bibliography Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=110106 Mathematical Model of Spontaneous Potential Well-Logging and Its Numerical Solutions [document électronique] / Tatsien Li ; Yongji Tan ; SpringerLink (Online service) ; Zhijie Cai ; Wei Chen ; Jingnong Wang . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2014 . - VII, 67 p. 28 illus., 14 illus. in color : online resource. - (SpringerBriefs in Mathematics, ISSN 2191-8198) .
ISBN : 978-3-642-41425-1
Langues : Anglais (eng)
Tags : Mathematics Physical geography Functional analysis Differential equations Numerical analysis Partial Differential Equations Geophysics Geodesy Numerical Analysis Functional Analysis Résumé : Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axi-symmetric situation the well-posedness of the corresponding mathematical model is proved and three efficient schemes of numerical solution are proposed, supported by a number of numerical examples to meet practical computation needs Note de contenu : Preface -- Modeling -- Properties of solutions -- Limiting behavior -- Techniques of solution -- Numerical simulation -- Bibliography Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=110106 Nonlinear Wave Equations / Tatsien Li / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2017)
Titre : Nonlinear Wave Equations Type de document : document électronique Auteurs : Tatsien Li ; Yi Zhou ; SpringerLink (Online service) Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2017 Collection : Series in Contemporary Mathematics, ISSN 2364-009X num. 2 Importance : XIV, 391 p. 2 illus Présentation : online resource ISBN/ISSN/EAN : 978-3-662-55725-9 Langues : Anglais (eng) Tags : Mathematics Difference equations Functional equations Partial differential equations Calculus of variations Partial Differential Equations Difference and Functional Equations Calculus of Variations and Optimal Control Optimization Résumé : This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle Note de contenu : Introduction -- Linear Wave functions -- Sobolev inequality with Decay -- Estimates for solutions for linear wave equation -- Estimates for composition Function Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=134648 Nonlinear Wave Equations [document électronique] / Tatsien Li ; Yi Zhou ; SpringerLink (Online service) . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2017 . - XIV, 391 p. 2 illus : online resource. - (Series in Contemporary Mathematics, ISSN 2364-009X; 2) .
ISBN : 978-3-662-55725-9
Langues : Anglais (eng)
Tags : Mathematics Difference equations Functional equations Partial differential equations Calculus of variations Partial Differential Equations Difference and Functional Equations Calculus of Variations and Optimal Control Optimization Résumé : This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle Note de contenu : Introduction -- Linear Wave functions -- Sobolev inequality with Decay -- Estimates for solutions for linear wave equation -- Estimates for composition Function Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=134648 Partial Differential Equations / Philippe Gaston Ciarlet / Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer (2014)
Titre : Partial Differential Equations : In Honor of the Scientific Heritage of Jacques-Louis Lions Type de document : document électronique Auteurs : Philippe Gaston Ciarlet (1938-....) ; Tatsien Li ; SpringerLink (Online service) ; Yvon Maday ; Jacques-Louis Lions (1928-2001), Dédicataire Editeur : Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer Année de publication : 2014 Importance : VIII, 429 p. 73 illus., 43 illus. in color Présentation : online resource ISBN/ISSN/EAN : 978-3-642-41401-5 Langues : Anglais (eng) Descripteurs : Échantillonnage Tags : Mathematics Differential equations Numerical analysis Mathematical optimization Partial Differential Equations Calculus of Variations and Optimal Control Optimization Numerical Analysis Résumé : This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing Note de contenu : Control and Nash Games with Mean Field Effect -- The Rain on Underground Porous Media Part I: Analysis of a Richards Model -- Finite Volume Multilevel Approximation of the Shallow Water Equations -- Non-gaussian Test Models for Prediction and State Estimation with Model Errors -- Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation -- Implicit Sampling, with Application to Data Assimilation -- Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: the Unfolding Approach -- Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation -- Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences -- On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev´e Equation: an Operator-Splitting Approach -- MsFEM `a la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems -- Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls -- Mixing Monte-Carlo and Partial Differential Equations for Pricing Options -- Increasing Powers in a Degenerate Parabolic Logistic Equation -- Composite Waves for a Cell Population System Modelling Tumor Growth and Invasion Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=110105 Partial Differential Equations : In Honor of the Scientific Heritage of Jacques-Louis Lions [document électronique] / Philippe Gaston Ciarlet (1938-....) ; Tatsien Li ; SpringerLink (Online service) ; Yvon Maday ; Jacques-Louis Lions (1928-2001), Dédicataire . - Berlin ; Heidelberg (DEU) ; New York ; Bâle (CHE) : Springer, 2014 . - VIII, 429 p. 73 illus., 43 illus. in color : online resource.
ISBN : 978-3-642-41401-5
Langues : Anglais (eng)
Descripteurs : Échantillonnage Tags : Mathematics Differential equations Numerical analysis Mathematical optimization Partial Differential Equations Calculus of Variations and Optimal Control Optimization Numerical Analysis Résumé : This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing Note de contenu : Control and Nash Games with Mean Field Effect -- The Rain on Underground Porous Media Part I: Analysis of a Richards Model -- Finite Volume Multilevel Approximation of the Shallow Water Equations -- Non-gaussian Test Models for Prediction and State Estimation with Model Errors -- Asymptotic Analysis in a Gas-Solid Combustion Model with Pattern Formation -- Implicit Sampling, with Application to Data Assimilation -- Periodic Homogenization for Inner Boundary Conditions with Equi-valued Surfaces: the Unfolding Approach -- Global Null Controllability of the 1-Dimensional Nonlinear Slow Diffusion Equation -- Sharp Interpolation Inequalities on the Sphere: New Methods and Consequences -- On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev´e Equation: an Operator-Splitting Approach -- MsFEM `a la Crouzeix-Raviart for Highly Oscillatory Elliptic Problems -- Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls -- Mixing Monte-Carlo and Partial Differential Equations for Pricing Options -- Increasing Powers in a Degenerate Parabolic Logistic Equation -- Composite Waves for a Cell Population System Modelling Tumor Growth and Invasion Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=110105