Dependence of solutions of nonsmooth differential-algebraic equations on parameters

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 classif...

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Bibliographic Details
Published in:Journal of Differential Equations Vol. 262; no. 3; pp. 2254 - 2285
Main Authors: Stechlinski, Peter G., Barton, Paul I.
Format: Journal Article
Language:English
Published: Elsevier Inc 05.02.2017
Subjects:
Consistent initialization
Existence
Generalized derivatives
Implicit function theorems
Semi-explicit
Uniqueness
34A12
26B10
Uniqueness
Generalized derivatives
Consistent initialization
Implicit function theorems
34A09
Existence
Semi-explicit
ISSN:0022-0396, 1090-2732
Online Access:Get full text
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2016.10.041