Dynamic contact with normal compliance wear and discontinuous friction coefficient

We apply the recent theory of evolution inclusions forset-valued pseudomonotone maps, developed in Kuttler and Shillor[Commun.Contemp.Math.,1(1999),pp.87–123]to the problem of dynamic frictional contact with normal compliance and wear. The friction coefficient is assumed to be slip rate dependent, and may be continuous, or discontinuous in the form of a graph with a vertical segment at the origin, representing the transition from the static to the dynamic value.The wear of the contacting surfaces is modeled by the Archard law.We prove the existence of a weak solution for the problem. We establish the uniqueness of the weak solution in the case when the friction coefficient is continuous. We also show that the problem with prescribed wear depends continuously on the wear.