Abstract Dissipative Hamiltonian Differential-Algebraic Equations Are Everywhere

Hans Zwart; Volker Mehrmann

doi:10.52825/dae-p.v2i.957

Authors

Hans Zwart University of Twente https://orcid.org/0000-0003-3451-7967
Volker Mehrmann Technische Universität Berlin https://orcid.org/0000-0001-5051-2870

DOI:

https://doi.org/10.52825/dae-p.v2i.957

Keywords:

Abstract Differential-Algebraic Equation, Closure Relation, Dissipative Hamiltonian System, Energy Based Modelling, Operator Pair, Regular Pair, Singular Pair

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.

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Abstract Dissipative Hamiltonian Differential-Algebraic Equations Are Everywhere

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