Hyperbolic Hemivariational Inequalities for Dynamic Viscoelastic Contact Problems

The paper deals with second order nonlinear evolution inclusions and their applications. First, we study an evolution inclusion involving Volterra-type integral operator which is considered within the framework of an evolution triple of spaces. We provide a result on the unique solvability of the Cauchy problem for the inclusion. Next, we examine a dynamic frictional contact problem of viscoelasticity for materials with long memory and derive a weak formulation of the model in the form of a hemivariational inequality. Then, we embed the hemivariational inequality into a class of second order evolution inclusions involving Volterra-type integral operator and indicate how the result on evolution inclusion is applicable to the model of the contact problem. We conclude with examples of the subdifferential boundary conditions for different types of frictional contact.