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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.
Mathematics --- PDAE
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Mithraism --- Mithracisme --- Ostia (Extinct city) --- Ostie (Ville ancienne) --- Religion --- Religion
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Arianism --- Jesus Christ
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Excavations (Archaeology) --- Fouilles (Archéologie) --- Sepphoris (Extinct city) --- Zippori (Israël) --- 902 <33 SEPPHORIS> --- Archeologie--Oud-Palestina. Judea--SEPPHORIS --- 902 <33 SEPPHORIS> Archeologie--Oud-Palestina. Judea--SEPPHORIS --- Fouilles (Archéologie) --- Zippori (Israël) --- Archaeological digs --- Archaeological excavations --- Digs (Archaeology) --- Excavation sites (Archaeology) --- Ruins --- Sites, Excavation (Archaeology) --- Archaeology --- Seffurieh (Extinct city) --- Sepphoris (Ancient city) --- Sepporis (Extinct city) --- Suffuriya (Extinct city) --- Tsipori (Extinct city) --- Tsiporim (Extinct city) --- Tsiporin (Extinct city) --- Tsippōrī (Extinct city) --- Ẓippori (Extinct city) --- Israel --- Antiquities
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This volume concerns the excavations at ancient Sepphoris, Israel, from 1983 to 1987. It contains a detailed report on the history of the site from ancient literary sources, a history of excavations and investigations, a report of the excavations against the tower ("the Citadel"), a report of other 5 x 5 m. probes near the Citadel, and eight 5 x 5 meter areas excavated in a building called a "church" or "basilica" in 1931, but now known to be a villa. The narrative incorporates details of small finds, coins, and pottery, with pottery drawings and architectural and stratigraphic drawings. The usefulness of the book is in reporting the archaeological data and integrating the archaeology into the ancient history of the city and of Galilee, of ancient Judaism, and of ancient Christianity.
Excavations (Archaeology) --- Archaeological digs --- Archaeological excavations --- Digs (Archaeology) --- Excavation sites (Archaeology) --- Ruins --- Sites, Excavation (Archaeology) --- Archaeology --- Sepphoris (Extinct city) --- Seffurieh (Extinct city) --- Sepphoris (Ancient city) --- Sepporis (Extinct city) --- Suffuriya (Extinct city) --- Tsipori (Extinct city) --- Tsiporim (Extinct city) --- Tsiporin (Extinct city) --- Tsippōrī (Extinct city) --- Ẓippori (Extinct city) --- Israel --- Antiquities
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Mithraism --- Antiquities --- Ostia (Extinct city)
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Mithraism. --- Ostia (Italy) --- Antiquities.
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Saunders, Ernest W. --- Bible. --- Criticism, interpretation, etc.
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Excavations (Archaeology) --- Israel --- Meron (Israel) --- Antiquities. --- Antiquities.
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