Noncoercive hyperbolic variational inequalities with applications to contact mechanics

In this paper we study a class of hyperbolic variational inequalities without a term depending on the first order derivative. Results on existence, uniqueness and regularity of a solution to the variational inequality are provided through the Rothe method. A frictional dynamic contact problem for viscoelastic material with noncoercive viscosity and subdifferential boundary conditions is studied as an illustrative application.