  We consider a differential quasivariational inequality for which we state and
prove the continuous dependence of the solution with respect to the data. This
convergence result allows us to prove the existence of at least one optimal
pair for an associated control problem. Finally, we illustrate our abstract
results in the study of a free boundary problem which describes the equilibrium
of a viscoelastic body in frictionless contact with a foundation made of a
rigid body coveblack by a rigid-elastic layer.
