Journal of Convex Analysis 30 (2023), No. 2, 659--742
Copyright Heldermann Verlag 2023
Various Perturbations and Relaxations of the Sweeping Process
Charles Castaing
Institut Montpelliérian A. Grothendick, Montpellier, France
charles.castaing@gmail.com
Lionel Thibault
Institut Montpelliérian A. Grothendick, Montpellier, France, France
and: Centro de Modelamiento Matematico, Universidad de Chile, Santiago, Chile
lionel.thibault@umontpellier.fr
The paper is concerned with diverse types of perturbations of dynamical sweeping processes along with their relaxation via Young measures. Skorohod-like problems with Volterra integro-differential perturbations are explored. Sweeping processes coupled with rough differential equations as well as with fractional differential equations are studied. Periodicity and asymptotic properties are also provided.
Keywords: Sweeping process, perturbation, prox-regular set, normal cone, relaxation, Skorohod problem, fractional derivative, fractional integral, rough signal, Young integral, Young measure, periodicity, asymptotic property.
MSC: 34A60, 49J52, 49J53.
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