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

Shih-Sen Chang (), Salahuddin, A. A. H. Ahmadini, Lin Wang and Gang Wang
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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

Mathematics, 2023, vol. 11, issue 9, 1-17

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.

Keywords: differential variational inequality; unilateral constraints; penalty method; Mosco convergence; viscoelastic rod; inverse strongly monotonicity; Lipschitz continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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