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Stability analysis for evolutionary variational-hemivariational inequalities with constraint sets

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Abstract

In this paper, we provide the stability analysis for an evolutionary variational-hemivariational inequality in the reflexive Banach space, whose data including the constraint set are perturbed. First, by using its perturbed data and the duality mapping, the perturbed and regularized problems for the evolutionary variational-hemivariational inequality are constructed, respectively. Then, by proving the unique solvability for the evolutionary variational-hemivariational inequality and its perturbed and regularized problems, we obtain two sequences called approximating sequences of the solution to the evolutionary variational-hemivariational inequality, and prove their strong convergence to the unique solution to the evolutionary variational-hemivariational inequality under different mild conditions.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11771067 and 11671282), the Applied Basic Project of Sichuan Province (Grant No. 2019YJ0204) and the Fundamental Research Funds for the Central Universities (Grant No. ZYGX2019J095).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yi-bin Xiao & Mou-tao Liu

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, China

    Tao Chen & Nan-jing Huang

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  1. Yi-bin Xiao
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  2. Mou-tao Liu
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  3. Tao Chen
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  4. Nan-jing Huang
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Correspondence to Yi-bin Xiao.

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Xiao, Yb., Liu, Mt., Chen, T. et al. Stability analysis for evolutionary variational-hemivariational inequalities with constraint sets. Sci. China Math. 65, 1469–1484 (2022). https://doi.org/10.1007/s11425-020-1838-2

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  • DOI: https://doi.org/10.1007/s11425-020-1838-2

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