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The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

Author

Listed:
  • Shih-Sen Chang

    (Center for General Education, China Medical University, Taichung 40402, Taiwan)

  • Salahuddin

    (Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia)

  • A. A. H. Ahmadini

    (Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia)

  • Lin Wang

    (College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Gang Wang

    (College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

Abstract

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed differential variational–hemivariational inequality problems with perturbed constraints and penalty coefficients. Then, for each perturbed inequality, we proved the unique solvability and convergence of the solutions to the problems. Following that, we proposed a mathematical model for a viscoelastic rod in unilateral contact equilibrium, where the unknowns were the displacement field and the history of the deformation. We used the abstract penalty method in the analysis of this inequality and provided the corresponding mechanical interpretations.

Suggested Citation

  • Shih-Sen Chang & Salahuddin & A. A. H. Ahmadini & Lin Wang & Gang Wang, 2023. "The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems," Mathematics, MDPI, vol. 11(9), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2066-:d:1133877
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