Evolution Hemivariational Inequality for a Class of Dynamic Viscoelastic Nonmonotone Frictional Contact Problems

In this paper, we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation. The friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction, and the Tresca models. The existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings.