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

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


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.


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

Mathematics Subject Classification

34H05 34K35 60H10 28A25 28C20 34G25 



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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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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