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Time-dependent elliptic quasi-variational-hemivariational inequalities: well-posedness and application

Author

Listed:
  • Tie-jun Jiang

    (University of Electronic Science and Technology of China)

  • Dong-ling Cai

    (University of Electronic Science and Technology of China)

  • Yi-bin Xiao

    (University of Electronic Science and Technology of China)

  • Stanisław Migórski

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

Abstract

In this paper we investigate a class of time-dependent quasi-variational-hemivariational inequalities (TDQVHVIs) of elliptic type in a reflexive separable Banach space, which is characterized by a constraint set depending on a solution. The solvability of the TDQVHVIs is obtained by employing a measurable selection theorem for measurable set-valued mappings, while the uniqueness of solution to the TDQVHVIs is guaranteed by enhancing the assumptions on the data. Then, under additional hypotheses, we deliver a continuous dependence result when all the data are subjected to perturbations. Finally, the applicability of the abstract results is illustrated by a frictional elastic contact problem with locking materials for which the existence and stability of the weak solutions is proved.

Suggested Citation

  • Tie-jun Jiang & Dong-ling Cai & Yi-bin Xiao & Stanisław Migórski, 2024. "Time-dependent elliptic quasi-variational-hemivariational inequalities: well-posedness and application," Journal of Global Optimization, Springer, vol. 88(2), pages 509-530, February.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:2:d:10.1007_s10898-023-01324-6
    DOI: 10.1007/s10898-023-01324-6
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    References listed on IDEAS

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    1. Akhtar A. Khan & Dumitru Motreanu, 2015. "Existence Theorems for Elliptic and Evolutionary Variational and Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1136-1161, December.
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