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Variational Analysis of a Dynamic Thermoviscoelastic Unilateral Contact Problem with Normal Damped Response and Friction

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Abstract

In this paper, we study a mathematical model that describes the dynamic frictional contact between the thermoviscoelastic body and the foundation. The contact condition is modeled by the so-called nonsmooth interface law involving unilateral constraints and subdifferential inclusions. The weak formulation of our mathematical model is a coupled system containing both parabolic and hyperbolic variational-hemivariational inequalities. As a result, we deliver its unique solvability by employing a surjectivity theorem for pseudomonotone operators, a fixed point argument for history-dependent operators and a mixed equilibrium formulation with suitably selected functions.

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Acknowledgements

The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the editor for their help too.

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Authors and Affiliations

  1. Department of Mathematics, Guizhou University, Guiyang, 550025, Guizhou, China

    Jianwei Hao & JinRong Wang

  2. Supercomputing Algorithm and Application Laboratory of Guizhou University and Gui’an Scientific Innovation Company, Guizhou University, Guiyang, 550025, Guizhou, China

    Jianwei Hao & JinRong Wang

  3. Department of Information and Statistics, Guangxi University of Finance and Economics, Guangxi, 530003, China

    Jiangfeng Han

Authors
  1. Jianwei Hao
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Correspondence to JinRong Wang.

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Communicated by Hedy Attouch

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This work is partially supported by the National Natural Science Foundation of China (12161015 and 12001120) and Guizhou Provincial Basic Research Program (Natural Science) [2023]034.

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Hao, J., Wang, J. & Han, J. Variational Analysis of a Dynamic Thermoviscoelastic Unilateral Contact Problem with Normal Damped Response and Friction. J Optim Theory Appl 199, 439–465 (2023). https://doi.org/10.1007/s10957-023-02295-0

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  • DOI: https://doi.org/10.1007/s10957-023-02295-0

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