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Evolutionary Quasi-variational Hemivariational Inequalities: Existence and Parameter Identification

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Abstract

This paper is concerned with an evolutionary quasi-variational hemivariational inequality in which both the convex and nonconvex energy functionals depend on the unknown solution. The inequality serves as a direct problem of the inverse problem of parameters identification. Employing a fixed point argument and tools from nonlinear analysis, we establish the solvability and weak compactness of the solution set to the direct problem. Then, general existence and weak compactness results for the regularized optimization inverse problem have been proved. Moreover, we illustrate the applicability of the results by an identification problem for an initial-boundary value problem of parabolic type with mixed multivalued and nonmonotone boundary conditions and a state constraint.

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Acknowledgements

This research is supported by the NSF of Guangxi, Grant No. 2021GXNSFFA220001, the Guangxi Science and Technology Program, Grant No. AD23023001, the NSF of China Grant No. 11901122, the Research Project of GXMZU Grant Nos. 2021MDKJ001 and gxun-chxb2022081, the Xiangsihu Young Scholars and Innovative Research Team of GXMZU Grant No. 2022GXUNXSHQN02, the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No. 823731 CONMECH, and the National Science Centre of Poland under Project No. 2021/41/B/ST1/01636.

Funding

Funding was provided by National natural science foudation of China (Grant no. 12071413).

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Authors and Affiliations

  1. College of Mathematics and Physics, and Center for Applied Mathematics of Guangxi, Guangxi Minzu University, Nanning, 530006, Guangxi, People’s Republic of China

    Zijia Peng

  2. College of Mathematics and Physics, and Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation, Guangxi Minzu University, Nanning, 530006, Guangxi, People’s Republic of China

    Guangkun Yang

  3. Center for Applied Mathematics of Guangxi, Yulin Normal University, Yulin, 537000, People’s Republic of China

    Zhenhai Liu

  4. College of Sciences, Beibu Gulf University, Qinzhou, 535000, Guangxi, People’s Republic of China

    Stanislaw Migórski

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

    Stanislaw Migórski

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  1. Zijia Peng
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Correspondence to Zhenhai Liu.

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Peng, Z., Yang, G., Liu, Z. et al. Evolutionary Quasi-variational Hemivariational Inequalities: Existence and Parameter Identification. Appl Math Optim 89, 32 (2024). https://doi.org/10.1007/s00245-023-10100-7

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