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State-Dependent Implicit Sweeping Process in the Framework of Quasistatic Evolution Quasi-Variational Inequalities

Author

Listed:
  • Samir Adly

    (Université de Limoges)

  • Tahar Haddad

    (Université de Jijel)

  • Ba Khiet Le

    (Universidad de O’Higgins)

Abstract

This paper deals with the existence and uniqueness of solutions for a class of state-dependent sweeping processes with constrained velocity in Hilbert spaces without using any compactness assumption, which is known to be an open problem. To overcome the difficulty, we introduce a new notion called hypomonotonicity-like of the normal cone to the moving set, which is satisfied by many important cases. Combining this latter notion with an adapted Moreau’s catching-up algorithm and a Cauchy technique, we obtain the strong convergence of approximate solutions to the unique solution, which is a fundamental property. Using standard tools from convex analysis, we show the equivalence between this implicit state-dependent sweeping processes and quasistatic evolution quasi-variational inequalities. As an application, we study the state-dependent quasistatic frictional contact problem involving viscoelastic materials with short memory in contact mechanics.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-018-1427-x
    DOI: 10.1007/s10957-018-1427-x
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    References listed on IDEAS

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    1. Khalid Addi & Daniel Goeleven, 2017. "Complementarity and Variational Inequalities in Electronics," Springer Optimization and Its Applications, in: Nicholas J. Daras & Themistocles M. Rassias (ed.), Operations Research, Engineering, and Cyber Security, pages 1-43, Springer.
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    Cited by:

    1. 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.

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