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Convergence Results for a Class of Generalized Second-Order Evolutionary Variational–Hemivariational Inequalities

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Abstract

In this paper, we deal with a class of second-order evolutionary history-dependent variational–hemivariational inequalities with constraint. The unique solvability of the considered second-order evolutionary inequality problem is established via a surjectivity result combined with a fixed point theorem. Moreover, we construct a regularized problem for such second-order evolutionary history-dependent variational–hemivariational inequality and show the convergence of the regularized solutions toward the solution of the original problem under some mild assumptions.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (12171070) and the Open Fund of National Center for Applied Mathematics in Sichuan (2023-KFJJ-02-001).

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Authors and Affiliations

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

    Dong-ling Cai & Yi-bin Xiao

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  1. Dong-ling Cai
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  2. Yi-bin Xiao
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Correspondence to Yi-bin Xiao.

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Communicated by Sofia Giuffre.

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Cai, Dl., Xiao, Yb. Convergence Results for a Class of Generalized Second-Order Evolutionary Variational–Hemivariational Inequalities. J Optim Theory Appl (2024). https://doi.org/10.1007/s10957-024-02396-4

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