On an existence and uniqueness theory for nonlinear differential-algebraic equations
- An existence and uniqueness theory is developed for general nonlinear and nonautonomous differential-algebraic equations (DAEs) by exploiting their underlying differential-geometric structure. A DAE is called regular if there is a unique nonautonomous vector field such that the solutions of the DAE and the solutions of the vector field are in one-to-one correspondence. Sufficient conditions for regularity of a DAE are derived in terms of constrained manifolds. Based on this differential-geometric characterization, existence and uniqueness results are stated for regular DAEs. Furthermore, our not ons are compared with techniques frequently used in the literature such as index and solvability. The results are illustrated in detail by means of a simple circuit example.
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| Author details: | Sebastian ReichORCiDGND |
|---|---|
| URN: | urn:nbn:de:kobv:517-opus-46706 |
| Publication series (Volume number): | Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 158) |
| Publication type: | Postprint |
| Language: | English |
| Publication year: | 1991 |
| Publishing institution: | Universität Potsdam |
| Release date: | 2010/09/13 |
| Source: | Circuits, Systems, and Signal Processing 10 (1991), 3, S. 343-359 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| License (German): |  Keine öffentliche Lizenz: Unter Urheberrechtsschutz |
| External remark: | first published in: Circuits, Systems, and Signal Processing10 (1991), 3, p. 343-359 doi: 10.1007/BF01187550 |
