Existence and Lyapunov Pairs for the Perturbed Sweeping Process Governed by a Fixed Set

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Abstract

The aim of this paper is to prove existence results for a class of sweeping processes in Hilbert spaces by using the catching-up algorithm. These processes are governed by ball-compact non autonomous sets. Moreover, a full characterization of nonsmooth Lyapunov pairs is obtained under very general hypotheses. We also provide a criterion for weak invariance. Some applications to hysteresis and crowd motion are given.

Keywords

Sweeping process Lyapunov pair Differential inclusions Invariance Normal cone 

Mathematics Subject Classification (2010)

34A60 49J52 34G25 49J53 93D30 

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Acknowledgements

The author wishes to express his deep gratitude to Prof. Abderrahim Jourani for his constant encouragement. Moreover, the author wishes to thank the referees for their helpful comments and suggestions which substantially improved the paper.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de Bourgogne Franche-ComtéDijonFrance
  2. 2.Departamento de Ingeniería MatemáticaUniversidad de ChileSantiagoChile
  3. 3.Instituto de Ciencias de la EducaciónUniversidad de O’HigginsRancaguaChile

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