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Chang Wang, Yi-Bin Xiao, Dong-Ling Cai, A class of mixed variational-hemivariational inequalities with history-dependent operators and time-dependent constraint sets

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DOI: 10.23952/jnva.9.2025.3.01

Volume 9, Issue 3, 1 June 2025, Pages 309-327

 

Abstract. The paper is devoted to investigating a new class of mixed variational-hemivariational inequalities (MVHVI) with history-dependent operators and time-dependent constraint sets. By employing a solvability result for static mixed variational-hemivariaitional inequalities in literature and a fixed-point theorem for history-dependent operators, we prove an existence result for solutions to the MVHVI based on which a convergence result of solutions to the MVHVI is established by considering its perturbation. Moreover, we apply the obtained abstract results to a quasistatic nonsmooth frictional contact problem with long memory, where the existence and convergence of weak solutions to the contact problem are derived.

 

How to Cite this Article:
C. Wang, Y.B. Xiao, D.L. Cai, A class of mixed variational-hemivariational inequalities with history-dependent operators and time-dependent constraint sets, J. Nonlinear Var. Anal. 9 (2025), 309-327.