INTEGRODIFFERENTIAL HEMIVARIATIONAL INEQUALITIES WITH APPLICATIONS TO VISCOELASTIC FRICTIONAL CONTACT
Abstract
We consider a class of abstract second-order evolutionary inclusions involving a Volterra-type integral term, for which we prove an existence and uniqueness result. The proof is based on arguments of evolutionary inclusions with monotone operators and the Banach fixed point theorem. Next, we apply this result to prove the solvability of a class of second-order integrodifferential hemivariational inequalities and, under an additional assumption, its unique solvability. Then we consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is dynamic, the material behavior is described with a viscoelastic constitutive law involving a long memory term and the contact is modelled with subdifferential boundary conditions. We derive the variational formulation of the problem which is of the form of an integrodifferential hemivariational inequality for the displacement field. Then we use our abstract results to prove the existence of a unique weak solution to the frictional contact model.
