## On the local qualitative behavior of differential-algebraic equations

- A theoretical famework for the investigation of the qualitative behavior of differential-algebraic equations (DAEs) near an equilibrium point is established. The key notion of our approach is the notion of regularity. A DAE is called regular locally around an equilibrium point if there is a unique vector field such that the solutions of the DAE and the vector field are in one-to-one correspondence in a neighborhood of this equili Drium point. Sufficient conditions for the regularity of an equilibrium point are stated. This in turn allows us to translate several local results, as formulated for vector fields, to DAEs that are regular locally around a g: ven equilibrium point (e.g. Local Stable and Unstable Manifold Theorem, Hopf theorem). It is important that ihese theorems are stated in terms of the given problem and not in terms of the corresponding vector field.

Author: | Sebastian Reich |
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URN: | urn:nbn:de:kobv:517-opus-46739 |

Series (Serial Number): | Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (paper 159) |

Document Type: | Postprint |

Language: | English |

Date of Publication (online): | 2010/09/13 |

Year of Completion: | 1995 |

Publishing Institution: | Universität Potsdam |

Release Date: | 2010/09/13 |

Source: | Circuits, Systems, and Signal Processing 14 (1995), 4, p. 427-443 |

Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |

Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Licence (German): | Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht |

Notes extern: | ﬁrst published in: Circuits, Systems, and Signal Processing 14 (1995), 4, p. 427-443 doi: 10.1007/BF01260330 |