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

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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.

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (12171070, 72033002), the Central Guidance on Local Science and Technology Development Fund of Sichuan Province (2021ZYD0002) and the Open Fund of National Center for Applied Mathematics in Sichuan (2023-KFJJ-02-001). The last author is supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement No. 823731 CONMECH, the Ministry of Science and Higher Education of Republic of Poland under Grant Nos. 4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019, and the National Science Centre of Poland under Project No. 2021/41/B/ST1/01636.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Sichuan, 611731, Chengdu, People’s Republic of China

    Tie-jun Jiang, Dong-ling Cai & Yi-bin Xiao

  2. Jagiellonian University in Krakow, Chair of Optimization and Control, ul. Lojasiewicza 6, 30348, Krakow, Poland

    Stanisław Migórski

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  1. Tie-jun Jiang
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  2. Dong-ling Cai
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  4. Stanisław Migórski
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Correspondence to Yi-bin Xiao.

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Jiang, Tj., Cai, Dl., Xiao, Yb. et al. Time-dependent elliptic quasi-variational-hemivariational inequalities: well-posedness and application. J Glob Optim 88, 509–530 (2024). https://doi.org/10.1007/s10898-023-01324-6

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