Schwenninger F. Systems Theory and PDEs. Open Problems, Recent Results,...2024

Textbook in PDF format

This volume presents recent advances and open problems in the cross section of infinite-dimensional systems theory and the modern treatment of PDEs. Chapters are based on talks and problem sessions from the first “Workshop on Systems Theory and PDEs” (WOSTAP), held at TU Bergakademie Freiberg in July 2022. The main topics covered include:
Differential algebraic equations
Port-Hamiltonian systems in both finite and infinite dimensions
Highly nonlinear equations related to elasticity/plasticity
Modeling of thermo-piezo-electromagnetism
Preface of Systems Theory and PDEs—Open Problems, Recent Results, and New Directions
On some Impedance Boundary Conditions for a Thermo-Piezo-Electromagnetic System
A Note on Some Non-Local Boundary Conditions and Their Use in Connection with Beltrami Fields
Spectral Theory for Schrödinger Operators on Compact Metric Graphs with δ and δ' Couplings: A Survey
Asymptotic Stability of Port-Hamiltonian Systems
Port-Hamiltonian Formulation of Oseen Flows
On the Equivalence of Geometric and Descriptor Representations of Linear Port-Hamiltonian Systems
On Differential-Algebraic Equations with Bounded Spectrum in Banach Spaces
BIBO Stability for Funnel Control: Semilinear Internal Dynamics with Unbounded Input and Output Operators
On Checking Lp-Admissibility for Parabolic Control Systems