A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation
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 insta...
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| Format: | Online |
| Sprache: | Englisch |
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Logos Verlag Berlin
2024
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| Online-Zugang: | OCN: 1437272661 |
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| _version_ | 1869529349189795840 |
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| author | Groh, Dennis |
| author_browse | Groh, Dennis |
| author_facet | Groh, Dennis |
| author_sort | Groh, Dennis |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-138571 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1385712025-07-31T11:45:00Z A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation Groh, Dennis Mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics 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. 2024-06-02T04:04:39Z 2024-06-02T04:04:39Z 2024-06-01T05:31:02Z 2024 book OCN: 1437272661 https://library.oapen.org/handle/20.500.12657/90740 https://directory.doabooks.org/handle/20.500.12854/138571 eng open access image/jpeg image/jpeg image/jpeg n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/90740/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/90740/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/90740/1/external_content.pdf Logos Verlag Berlin Logos Verlag Berlin 04b263a1-7fba-4491-9eae-1c394ac42fc3 Knowledge Unlatched (KU) KU Open Services Logos Verlag Berlin open access |
| spellingShingle | Mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics Groh, Dennis A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation |
| title | A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation |
| title_full | A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation |
| title_fullStr | A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation |
| title_full_unstemmed | A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation |
| title_short | A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation |
| title_sort | coupled system of differential algebraic equation and hyperbolic partial differential equation |
| topic | Mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics |
| topic_facet | Mathematics bic Book Industry Communication::P Mathematics & science::PB Mathematics |
| url | OCN: 1437272661 |
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