Title | Dependence of solutions of nonsmooth differential-algebraic equations on parameters |

Publication Type | Journal Article |

Year of Publication | 2017 |

Authors | Stechlinski PG, Barton PI |

Journal | Journal of Differential Equations |

Volume | 262 |

Issue | 3 |

Pagination | 2254–2285 |

Abstract | The well-posedness of nonsmooth differential-algebraic equations (DAEs) is investigated. More specifically, semi-explicit DAEs with Carathéodory-style assumptions on the differential right-hand side functions and local Lipschitz continuity assumptions on the algebraic equations. The DAEs are classified as having differential index one in a generalized sense; solution regularity is formulated in terms of projections of generalized (Clarke) Jacobians. Existence of solutions is derived under consistency and regularity of the initial data. Uniqueness of a solution is guaranteed under analogous Carathéodory ordinary-differential equation uniqueness assumptions. The continuation of solutions is established and sufficient conditions for continuous and Lipschitzian parametric dependence of solutions are also provided. To accomplish these results, a theoretical tool for analyzing nonsmooth DAEs is provided in the form of an extended nonsmooth implicit function theorem. The findings here are a natural extension of classical results and lay the foundation for further theoretical and computational analyses of nonsmooth DAEs. |

URL | https://authors.elsevier.com/a/1UF3a50j-W3AE |

DOI | 10.1016/j.jde.2016.10.041 |

# Dependence of solutions of nonsmooth differential-algebraic equations on parameters

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