Logos Verlag Berlin - Neuerscheinungen - MathematikNeuerscheinungen im Fachgebiet Mathematik im Logos Verlag Berlin
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Dennis Groh : A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation. Analysis and Optimal Control
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http://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=5773&lng=deu&id=Sun, 26 May 2024 02:00:00 +0200
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 ...