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We consider a differential quasivariational inequality for which we state andprove the continuous dependence of the solution with respect to the data. Thisconvergence result allows us to prove the existence of at least one optimalpair for an associated control problem. Finally, we illustrate our abstractresults in the study of a free boundary problem which describes the equilibriumof a viscoelastic body in frictionless contact with a foundation made of arigid body coveblack by a rigid-elastic layer.

Optimal control of differential quasivariational inequalities with applications in contact mechanics