Long-time behavior of delay differential quasi-variational–hemivariational inequalities and application to contact problems

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.