A Coupled System of Differential-Algebraic Equation and Hyperbolic Partial Differential Equation Analysis and Optimal Control

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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Bibliographic Details
Main Author: Groh, Dennis
Format: eBook
Language:English
Published: Berlin/Germany Logos Verlag Berlin 2024
Subjects:
Abstract DAE
Applied mathematics
Book Industry Communication
Calculus
Calculus and mathematical analysis
Differential calculus and equations
Electronics and communications engineering
Electronics engineering
Electronics: circuits and components
Existence and Uniqueness
Functional analysis and transforms
Mathematical modelling
Mathematics
Mathematics & science
Mathematics and Science
Maths for scientists
Optimal Control
Optimization
PDAE
Science: general issues
Technology, Engineering, Agriculture, Industrial processes
Wave Equation
ISBN:9783832557737, 3832557733
Online Access:Get full text
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Summary: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.
Bibliography:MODID-49e8e26250d:KU Open Services
MODID-00000000488:Knowledge Unlatched
MODID-da78cf4e7ff:Logos Verlag Berlin
ISBN:9783832557737
3832557733
DOI:10.30819/5773