Hyperbolic hemivariational inequalities controlled by evolution equations with application to adhesive contact model

A system which couples an abstract hemivariational inequality of hyperbolic type and an evolution equation in a Banach space is studied. The global existence of the system is established by exploiting the Rothe method. An application to a dynamic adhesive viscoelastic contact problem with friction is provided for which results on existence and regularity of weak solutions are proved.