In this article, we study a class of differential quasi-variational–hemivariational inequalities involving time delays. We establish new systems and prove the solvability and the existence of decay solutions. Moreover, we are concerned with long-time behavior of solutions by showing the existence of a compact global attractor to m-semiflow associated with delay differential quasi-variational–hemivariational inequalities. An application to the contact problems driven by dynamic systems is discussed to demonstrate our theoretical results.

中文翻译：

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时滞微分准变分-半变分不等式的长期行为及其在接触问题中的应用

在本文中，我们研究了一类涉及时间延迟的微分拟变分半变分不等式。我们建立新系统并证明衰变解的可解性和存在性。此外，我们通过证明与时滞微分准变分半变分不等式相关的m半流的紧全局吸引子的存在来关注解的长期行为。讨论了动态系统驱动的接触问题的应用，以证明我们的理论结果。