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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

Lionel Thibault
Institut Montpelliérian A. Grothendick, Montpellier, France, France
and: Centro de Modelamiento Matematico, Universidad de Chile, Santiago, Chile

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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