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Well-Posedness of History/State-Dependent Implicit Sweeping Processes

Author

Listed:
  • Shengda Zeng

    (Yulin Normal University
    Jagiellonian University in Krakow, Chair of Optimization and Control)

  • Emilio Vilches

    (Universidad de O’Higgins)

Abstract

This paper is devoted to the study of a new class of implicit state-dependent sweeping processes with history-dependent operators. Based on the methods of convex analysis, we prove the equivalence of the history/state dependent implicit sweeping process and a nonlinear differential equation, which, through a fixed point argument for history-dependent operators, enables us to prove the existence, uniqueness, and continuous dependence of the solution in a very general framework. Moreover, we present some new convergence results with respect to perturbations in the data, including perturbations of the associated moving sets. Finally, the theoretical results are applied to prove the well-posedness of a history-dependent quasi-static contact problem.

Suggested Citation

  • Shengda Zeng & Emilio Vilches, 2020. "Well-Posedness of History/State-Dependent Implicit Sweeping Processes," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 960-984, September.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01730-w
    DOI: 10.1007/s10957-020-01730-w
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    References listed on IDEAS

    as
    1. Samir Adly & Tahar Haddad & Ba Khiet Le, 2019. "State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 473-493, August.
    2. Abderrahim Jourani & Emilio Vilches, 2017. "Moreau-Yosida Regularization of State-Dependent Sweeping Processes with Nonregular Sets," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 91-116, April.
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    Cited by:

    1. Savin Treanţă, 2022. "Well-Posedness Results of Certain Variational Inequalities," Mathematics, MDPI, vol. 10(20), pages 1-15, October.

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