Abstract Dissipative Hamiltonian Differential-Algebraic Equations Are Everywhere

Authors

Abstract

In this paper we study the representation of partial differential equations (PDEs) as abstract differential-algebraic equations (DAEs) with dissipative Hamiltonian structure (adHDAEs). We show that these systems not only arise when there are constraints coming from the underlying physics, but many standard PDE models can be seen as an adHDAE on an extended state space. This reflects the fact that models often include closure relations and structural properties. We present a unifying operator theoretic approach to analyze the properties of such operator equations and illustrate this by several applications.

Citation

Journal: DAE Panel
Year: 2024
Volume: 2
Issue:
Pages:
Publisher: TIB Open Publishing
DOI: 10.52825/dae-p.v2i.957

BibTeX

@article{Zwart_2024,
  title={{Abstract Dissipative Hamiltonian Differential-Algebraic Equations Are Everywhere}},
  volume={2},
  ISSN={2939-9084},
  DOI={10.52825/dae-p.v2i.957},
  journal={DAE Panel},
  publisher={TIB Open Publishing},
  author={Zwart, Hans and Mehrmann, Volker},
  year={2024}
}

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References

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