M. Shillor, M. Sofonea and J. J. Telega,

We consider a quasistatic problem of frictional contact between a
deformable body and a moving foundation. The material is assumed to
have nonlinear viscoelastic behavior. The contact is modeled with normal
compliance and the associated law of dry friction. The wear takes place
on a part of the contact surface, and the wear particles rate of production
is described by the Archard differential condition. The main novelty in the
model is the diffusion of the wearparticles over the potential contact surface.
Such phenomena arise in orthopaedic biomechanics where the wear debris
diffuse and influence the properties of joint prosthesis and implants. We derive
a weak formulation of the model which is given by a coupled system with an
evolutionary variational inequality and a nonlinear evolutionary variational equation.
We prove that, under a smallness assumption on some of the data, there exists
a unique weak solution for the model.