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Long-time behavior of delay differential quasi-variational–hemivariational inequalities and application to contact problems

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Abstract

In this article, we study a class of differential quasi-variational–hemivariational inequalities involving time delays. We establish new systems and prove the solvability and the existence of decay solutions. Moreover, we are concerned with long-time behavior of solutions by showing the existence of a compact global attractor to m-semiflow associated with delay differential quasi-variational–hemivariational inequalities. An application to the contact problems driven by dynamic systems is discussed to demonstrate our theoretical results.

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Acknowledgements

The final version of this work was completed when the first author, Van Anh, visited Rochester Institute of Technology, USA, based on Abel Visiting Scholarship Program of International Mathematical Union. She would like to take this oppotunity to thank the Niels Hendrik Abel Board and Rochester Institute of Technology for their support and hospitality. Nguyen Thi Van Anh was funded by the Postdoctoral Scholarship Programme of Vingroup Innovation Foundation (VINIF), Institute of Big Data, code VINIF.2023.STS.51.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, No. 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam

    Nguyen Thi Van Anh

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, No. 18 Hoang Quoc Viet, Hanoi, Vietnam

    Nguyen Thi Van Anh

  3. East Asia University of Technology, Trinh Van Bo, Nam Tu Liem, Hanoi, Vietnam

    Tran Van Thuy

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  1. Nguyen Thi Van Anh
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Correspondence to Nguyen Thi Van Anh.

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Van Anh, N.T., Van Thuy, T. Long-time behavior of delay differential quasi-variational–hemivariational inequalities and application to contact problems. Z. Angew. Math. Phys. 75, 55 (2024). https://doi.org/10.1007/s00033-024-02202-1

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