Quasistatic frictional contact and wear of a beam

A problem of frictional contact between an elastic beam and a moving founda tion and the resulting wear of the beam is considered. The process is assum ed to be quasistatic, the contact is modeled with normal compliance, and th e wear is described by the Archard law. Existence and uniqueness of the wea k solution for the problem is proved using the theory of strongly monotone operators and the Cauchy-Lipschitz theorem. It is also shown that growth of the the wear function is at most linear. Finally, a numerical approach to the problem is considered using a time semi-discrete scheme. The existence of the unique solution for the discretized scheme is established, and error estimates on the approximate solutions are derived.