A CLASS OF MIXED VARIATIONAL-HEMIVARIATIONAL INEQUALITIES WITH HISTORY-DEPENDENT OPERATORS AND TIME-DEPENDENT CONSTRAINT SETS

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.