Systems Theory and PDEs Open Problems, Recent Results, and New Directions

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

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 Schrodinger Operators on Compact Metric Graphs with d AND d' Couplings: A Survey.- Asymptotic Stability of port-Hamiltonian Systems.- Port-Hamiltonian Formulation of Oseen Floes.- 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.

Marcus Waurick is University Professor and Chair for Partial Differential Equations at TU Bergakademie Freiberg, Germany.

Felix Schwenninger  is Associate Professor at the University of Twente, Enschede, Netherlands.