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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Metadaten
Author:Sebastian Reich
URN:urn:nbn:de:kobv:517-opus-46706
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe, ISSN 1866-8372 (paper 158)
Document Type:Postprint
Language:English
Date of Publication (online):2010/09/13
Year of Completion: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
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:
first published in:
Circuits, Systems, and Signal Processing10 (1991), 3, p. 343-359
doi: 10.1007/BF01187550