Viscoelastic sliding contact problems with wear

We consider a mathematical model which describes the sliding contact with wear between a viscoelastic body and a rigid moving foundation. We consider both the dynamic and quasi-static cases and we model the wear with a version of Archardʹs law. We derive the variational formulation of the model and prove existence and uniqueness results. The proofs are based on arguments of evolution equations with monotone operators and Banachʹs fixed-point theorem, in the case of the dynamical model, and on Cauchy-Lipschitz theorem in the case of the quasi-static model. We also establish the continuous dependence of the solution with respect to parameters related to the velocity of the moving foundation.