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A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation
dc.contributor.authorGroh, Dennis
dc.date.accessioned2024-07-10T08:43:07Z
dc.date.available2024-07-10T08:43:07Z
dc.date.issued2024none
dc.identifier.isbn978-3-8325-5773-7
dc.identifier.urihttp://edoc.hu-berlin.de/18452/29717
dc.descriptionThe publication of this work was supported by the Open Access Publication Fund of Humboldt-Universität zu Berlin.none
dc.description.abstractCoupled 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.eng
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights(CC BY 4.0) Attribution 4.0 Internationalger
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectdifferential-algebraic equationeng
dc.subjectmatrix-induced linear operatorseng
dc.subjectoptimal control problemeng
dc.subjectdecoupling strategyeng
dc.subject.ddc510 Mathematiknone
dc.titleA Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equationnone
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/29717-2
dc.identifier.doihttp://dx.doi.org/10.18452/29097
dc.type.versionpublishedVersionnone
local.edoc.pages154none
local.edoc.type-nameBuch
dc.title.subtitleAnalysis and Optimal Controlnone
dcterms.bibliographicCitation.doi10.30819/5773
dcterms.bibliographicCitation.originalpublishernameLogos Verlagnone
dcterms.bibliographicCitation.originalpublisherplaceBerlinnone
bua.departmentMathematisch-Naturwissenschaftliche Fakultätnone

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