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Optimal Control for Time-Dependent Variational–Hemivariational Inequalities

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Abstract

The present work is intended to investigate optimal control for time-dependent variational–hemivariational inequalities in which the constraint set depends on time. Based on the existence, uniqueness and boundedness of the solution to the inequality, we deliver two continuous dependence results with respect to the time, and then, an existence result for an optimal control problem is presented. Finally, a semipermeability problem and a quasistatic frictional contact problem are given to illustrate our main results.

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Funding

The work was supported by the Natural Science Foundation of Guangxi Province (No. 2019GXNSFBA185005), the Start-up Project of Scientific Research on Introducing talents at school level in Guangxi University for Nationalities (No. 2019KJQD04) and the Xiangsihu Young Scholars Innovative Research Team of Guangxi University for Nationalities (No. 2019RSCXSHQN02).

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Guangxi University for Nationalities, Nanning, 530006, Guangxi Province, People’s Republic of China

    Biao Zeng

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  1. Biao Zeng
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The author read and approved the final manuscript.

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Correspondence to Biao Zeng.

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The author declares to have no competing interests.

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Communicated by Rosihan M. Ali.

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Zeng, B. Optimal Control for Time-Dependent Variational–Hemivariational Inequalities. Bull. Malays. Math. Sci. Soc. 44, 1961–1977 (2021). https://doi.org/10.1007/s40840-020-01042-2

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  • DOI: https://doi.org/10.1007/s40840-020-01042-2

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