Optimal Control for Time-Dependent Variational–Hemivariational Inequalities

Abstract

The present work is intended to investigate optimal control for time-dependent variational–hemivariational inequalities in which the constraint set depends on time. Based on the existence, uniqueness and boundedness of the solution to the inequality, we deliver two continuous dependence results with respect to the time, and then, an existence result for an optimal control problem is presented. Finally, a semipermeability problem and a quasistatic frictional contact problem are given to illustrate our main results.