Dependence of solutions of nonsmooth differential-algebraic equations on parameters
| Autor: | Paul I. Barton, Peter Stechlinski |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
021103 operations research Applied Mathematics Mathematical analysis Mathematics::Optimization and Control 0211 other engineering and technologies 02 engineering and technology Lipschitz continuity Implicit function theorem Continuation Algebraic equation 020901 industrial engineering & automation Uniqueness Differential algebraic equation Analysis Differential (mathematics) Parametric statistics Mathematics |
| Zdroj: | Journal of Differential Equations. 262:2254-2285 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2016.10.041 |
| Popis: | The well-posedness of nonsmooth differential-algebraic equations (DAEs) is investigated. More specifically, semi-explicit DAEs with Caratheodory-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 Caratheodory 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. |
| Databáze: | OpenAIRE |
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