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Linear port-Hamiltonian systems on multidimensional spatial domains / vorgelegt von Nathanael Skrepek. Wuppertal, Novenmber 2021
Content
Symbols
Introduction
Important for Cherry Picker
Preliminaries
Distributions
Lipschitz Boundary
Dual Pairs
Linear Relations
Basics
Adjoint Linear Relations
Skew-symmetry and Dissipativity on Hilbert Spaces
Boundary Triples
Strongly Continuous Semigroups
Port-Hamiltonian Systems
Differential Operators
Port-Hamiltonian Systems
The Wave Equation as port-Hamiltonian System
Maxwell's Equations
Mindlin Plate Model
Quasi Gelfand Triples
Motivation
Definition and Results
Quasi Gelfand Triple with Hilbert Spaces
Quasi Gelfand Triples and Boundary Triples
Boundary Spaces
Boundary Spaces for
Abstract Approach
Boundary Triple for a port-Hamiltonian System
Conclusion
Boundary Control and Observation Systems
Basics
Port-Hamiltonian System as Boundary Control and Observation System
Wave Equation
Maxwell's Equations
Mindlin Plate Model
Stabilization of the Wave Equation
Introduction
Port-Hamiltonian Formulation of the System
Stability Results
Conclusion
Compact Embedding for `3́9`42`"̇613A``45`47`"603Adiv-`3́9`42`"̇613A``45`47`"603Arot Systems
Introduction
Notations
Preliminaries
Compact Embeddings
Applications
Friedrichs/Poincaré Type Estimates
A div-curl Lemma
Maxwell's Equations with Mixed Impedance Type Boundary Conditions
Appendix
Gårding Inequalities
Solution Theory for the Wave Equation
Uncategorized
Bibliography