Analysis of a dynamic contact problem with friction, damage and adhesion

We study a dynamic contact problem for viscoelastic materials with damage. The contact is modelled with Tresca’s friction law and a first order differential equation which describes adhesion effect of contact surfaces; the damage of the material is described by a function whose evolution is governed by a parabolic inclusion. Under appropriate assumptions, we provide a variational formulation of the mechanical problem and establish the existence and uniqueness of a weak solution.