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A Coupled System of Differential-algebraic Equation and Hyperbolic Partial Differential Equation: Analysis and Optimal Control - Couverture souple
Synopsis
Coupled systems of differential-algebraic equations (DAEs) and partial differential equations (PDEs) appear in various fields of applications such as electrical engineering, bio-mathematics, or multi-physics. They are of particular interest for the modeling and simulation of flow networks, for instance energy transport networks. In this thesis, we discuss a system in which an abstract DAE and a second order hyperbolic PDE are coupled through nonlinear coupling functions. The analysis presented is split into two parts: In the first part, we introduce the concept of matrix-induced linear operators which arise naturally in the context of abstract DAEs but have surprisingly not been discussed in literature on abstract DAEs so far. We also present a novel index-1-like criterion that allows to separate dynamical and non-dynamical parts of the abstract DAE while allowing for a considerable reduction of required assumptions, compared to existing theoretical results for abstract DAEs. In the second part, we build upon the developed techniques. We show how to combine the theoretical frameworks for abstract DAEs and second order hyperbolic PDEs in a way such that both parts of the solution are of similar regularity. We then use a fixed-point approach to prove existence and uniqueness of local as well as global solutions to the coupled system. In the last part of this thesis, we throw a glance at a related optimal control problem and prove existence of a global minimizer.
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A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation: Analysis and Optimal Control
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Logos Verlag Berlin GmbH, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
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Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation : Analysis and Optimal Control
Edité par
Logos Verlag Berlin, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
Neuf
Couverture souple
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Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation : Analysis and Optimal Control
Edité par
Logos Verlag Berlin, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
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Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation
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A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation: Analysis and Optimal Control
Edité par
Logos Verlag Berlin GmbH, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
Neuf
Couverture souple
Vendeur : Kennys Bookstore, Olney, MD, Etats-Unis
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A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation (Paperback)
Edité par
Logos Verlag Berlin GmbH, Berlin, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
Neuf
Paperback
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Paperback. Etat : new. Paperback. Coupled systems of differential-algebraic equations (DAEs) and partial differential equations (PDEs) appear in various fields of applications such as electrical engineering, bio-mathematics, or multi-physics. They are of particular interest for the modeling and simulation of flow networks, for instance energy transport networks. In this thesis, we discuss a system in which an abstract DAE and a second order hyperbolic PDE are coupled through nonlinear coupling functions.The analysis presented is split into two parts: In the first part, we introduce the concept of matrix-induced linear operators which arise naturally in the context of abstract DAEs but have surprisingly not been discussed in literature on abstract DAEs so far. We also present a novel index-1-like criterion that allows to separate dynamical and non-dynamical parts of the abstract DAE while allowing for a considerable reduction of required assumptions, compared to existing theoretical results for abstract DAEs.In the second part, we build upon the developed techniques. We show how to combine the theoretical frameworks for abstract DAEs and second order hyperbolic PDEs in a way such that both parts of the solution are of similar regularity. We then use a fixed-point approach to prove existence and uniqueness of local as well as global solutions to the coupled system.In the last part of this thesis, we throw a glance at a related optimal control problem and prove existence of a global minimizer. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. N° de réf. du vendeur 9783832557737
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A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation (Paperback)
Edité par
Logos Verlag Berlin GmbH, Berlin, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
Neuf
Paperback
Vendeur : Grand Eagle Retail, Mason, OH, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Paperback. Etat : new. Paperback. Coupled systems of differential-algebraic equations (DAEs) and partial differential equations (PDEs) appear in various fields of applications such as electrical engineering, bio-mathematics, or multi-physics. They are of particular interest for the modeling and simulation of flow networks, for instance energy transport networks. In this thesis, we discuss a system in which an abstract DAE and a second order hyperbolic PDE are coupled through nonlinear coupling functions.The analysis presented is split into two parts: In the first part, we introduce the concept of matrix-induced linear operators which arise naturally in the context of abstract DAEs but have surprisingly not been discussed in literature on abstract DAEs so far. We also present a novel index-1-like criterion that allows to separate dynamical and non-dynamical parts of the abstract DAE while allowing for a considerable reduction of required assumptions, compared to existing theoretical results for abstract DAEs.In the second part, we build upon the developed techniques. We show how to combine the theoretical frameworks for abstract DAEs and second order hyperbolic PDEs in a way such that both parts of the solution are of similar regularity. We then use a fixed-point approach to prove existence and uniqueness of local as well as global solutions to the coupled system.In the last part of this thesis, we throw a glance at a related optimal control problem and prove existence of a global minimizer. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9783832557737
Quantité disponible : 1 disponible(s)
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A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation (Paperback)
Edité par
Logos Verlag Berlin GmbH, Berlin, 2024
ISBN 10 : 3832557733
ISBN 13 : 9783832557737
Neuf
Paperback
Vendeur : AussieBookSeller, Truganina, VIC, Australie
Évaluation du vendeur 5 sur 5 étoiles
Paperback. Etat : new. Paperback. Coupled systems of differential-algebraic equations (DAEs) and partial differential equations (PDEs) appear in various fields of applications such as electrical engineering, bio-mathematics, or multi-physics. They are of particular interest for the modeling and simulation of flow networks, for instance energy transport networks. In this thesis, we discuss a system in which an abstract DAE and a second order hyperbolic PDE are coupled through nonlinear coupling functions.The analysis presented is split into two parts: In the first part, we introduce the concept of matrix-induced linear operators which arise naturally in the context of abstract DAEs but have surprisingly not been discussed in literature on abstract DAEs so far. We also present a novel index-1-like criterion that allows to separate dynamical and non-dynamical parts of the abstract DAE while allowing for a considerable reduction of required assumptions, compared to existing theoretical results for abstract DAEs.In the second part, we build upon the developed techniques. We show how to combine the theoretical frameworks for abstract DAEs and second order hyperbolic PDEs in a way such that both parts of the solution are of similar regularity. We then use a fixed-point approach to prove existence and uniqueness of local as well as global solutions to the coupled system.In the last part of this thesis, we throw a glance at a related optimal control problem and prove existence of a global minimizer. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. N° de réf. du vendeur 9783832557737
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