In this paper, we study a class of subdifferential evolution inclusions involving history-dependent operators. First, we improve an existence and uniqueness theorem and prove the continuous dependence result in the weak topologies. Next, we establish the existence of optimal solution to an optimal control problem for the evolution inclusion. Finally, we illustrate the results by an example of an optimal control of a dynamic frictional contact problem in mechanics, whose weak formulation is the evolution variational inequality.

中文翻译：

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历史相关演化内含物的最佳控制与摩擦接触应用

在本文中，我们研究了一类涉及历史相关算子的亚微分演化包含。首先，我们改进了存在唯一性定理并证明了弱拓扑中的连续依赖结果。接下来，我们建立进化包含的最优控制问题的最优解的存在性。最后，我们通过一个力学中动态摩擦接触问题的最优控制的例子来说明结果，其弱公式是演化变分不等式。