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

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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.

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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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Authors and Affiliations

  1. Université Mohammed Seddik Benyahia, Jijel, Algérie

    Fatine Aliouane & Dalila Azzam-Laouir

  2. IMAG, Univ Montpellier, CNRS, Montpellier, France

    Charles Castaing

  3. CMAFcIO, Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, 1749-016, Campo Grande, Lisboa, Portugal

    Manuel D. P. Monteiro Marques

Authors
  1. Fatine Aliouane
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  2. Dalila Azzam-Laouir
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  3. Charles Castaing
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  4. Manuel D. P. Monteiro Marques
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Correspondence to Manuel D. P. Monteiro Marques.

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Aliouane, F., Azzam-Laouir, D., Castaing, C. et al. Second-Order Time and State-Dependent Sweeping Process in Hilbert Space. J Optim Theory Appl 182, 153–188 (2019). https://doi.org/10.1007/s10957-018-01455-x

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