Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation

Analysis and Optimal Control

By (author) Dennis Groh

Book cover: Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation

Extent: 150 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

Paperback (Published)

(May 2024)

ISBN: 9783832557737

8.27 x 11.65 inches

Price: $60.00

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Synopsis
Contributing Authors

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.

By (author) Dennis Groh

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Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation

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