Abstract 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 covered by a rigid-elastic layer.

中文翻译：

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微分拟变分不等式的优化控制在接触力学中的应用

摘要 我们考虑一个微分拟变分不等式，我们陈述并证明了解对数据的连续依赖性。这个收敛结果使我们能够证明至少存在一对相关控制问题的最佳对。最后，我们说明了我们在自由边界问题研究中的抽象结果，该问题描述了粘弹性体与由刚体覆盖的刚体-弹性层构成的基础无摩擦接触的平衡。