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Second-Order Time and State-Dependent Sweeping Process in Hilbert Space

  • Fatine Aliouane
  • Dalila Azzam-Laouir
  • Charles Castaing
  • Manuel D. P. Monteiro MarquesEmail author
Article
  • 32 Downloads

Abstract

Using an explicit catching-up algorithm, we prove the existence of absolutely continuous as well as bounded variation continuous solutions to a second-order perturbed Moreau’s sweeping process with the normal cone of a subsmooth moving set, which depends both on the time and on the state.

Keywords

Absolutely continuous Bounded variation Carathéodory perturbation Fréchet normal cone Set-valued perturbation Subsmoothness Sweeping process 

Mathematics Subject Classification

34H05 34K35 60H10 28A25 28C20 34G25 

Notes

Acknowledgements

M. D. P. Monteiro Marques was partially supported by National Funding from FCT—Fundação para a Ciência e Tecnologia, under the Project UID/MAT/04561/2013.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Mohammed Seddik BenyahiaJijelAlgérie
  2. 2.IMAG, Univ Montpellier, CNRSMontpellierFrance
  3. 3.CMAFcIO, Departamento de MatemáticaFaculdade de Ciências da Universidade de LisboaCampo GrandePortugal

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