Abstract dissipative Hamiltonian differential-algebraic equations are everywhere
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913353418407936 |
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| author | Mehrmann, Volker Zwart, Hans |
| author_facet | Mehrmann, Volker Zwart, Hans |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03091 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Abstract dissipative Hamiltonian differential-algebraic equations are everywhere Mehrmann, Volker Zwart, Hans Functional Analysis Optimization and Control 37L05, 37L20, 47D06, 47F05, 93B28, 93C05 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. |
| title | Abstract dissipative Hamiltonian differential-algebraic equations are everywhere |
| topic | Functional Analysis Optimization and Control 37L05, 37L20, 47D06, 47F05, 93B28, 93C05 |
| url | https://arxiv.org/abs/2311.03091 |