nonsmooth mechanics
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2017 ◽  
Vol 23 (4) ◽  
pp. 1293-1329 ◽  
Author(s):  
Samir Adly ◽  
Florent Nacry ◽  
Lionel Thibault

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.



Author(s):  
Bernard Brogliato
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PAMM ◽  
2015 ◽  
Vol 15 (1) ◽  
pp. 73-74
Author(s):  
Thorsten Schindler ◽  
Johannes Mayet ◽  
Philipp Seiwald
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