Discontinuous sweeping process with prox regular sets
Author
dc.contributor.author
Adly, Samir
Author
dc.contributor.author
Nacry, Florent
Author
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Thibault, Lionel
Admission date
dc.date.accessioned
2018-07-03T14:40:10Z
Available date
dc.date.available
2018-07-03T14:40:10Z
Publication date
dc.date.issued
2017
Cita de ítem
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ESAIM-Control Optimisation and Calculus of Variations, 23(4): 1293-1329
es_ES
Identifier
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10.1051/cocv/2016053
Identifier
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https://repositorio.uchile.cl/handle/2250/149414
Abstract
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In this paper, we study the well-posedness (in the sense of existence and uniqueness of a solution) of a discontinuous sweeping process involving prox-regular sets in Hilbert spaces. The variation of the moving set is controlled by a positive Radon measure and the perturbation is assumed to satisfy a Lipschitz property. The existence of a solution with bounded variation is achieved thanks to the Moreau's catching-up algorithm adapted to this kind of problem. Various properties and estimates of jumps of the solution are also provided. We give sufficient conditions to ensure the uniform prox-regularity when the moving set is described by inequality constraints. As an application, we consider a nonlinear differential complementarity system which is a combination of an ordinary differential equation with a nonlinear complementarily condition. Such problems appear in many areas such as nonsmooth mechanics, nonregular electrical circuits and control systems.