  We establish existence of long-time solutions to a dynamic problem of
bilateral contact between a rigid surface and a viscoelastic body, subject to
rate-and-state friction. The term rate-and-state friction is used here to refer
to a set of functions and equations satisfying conditions which rule out the
slip law but do cover the ageing law, and thus at least one of the
rate-and-state friction laws commonly used in the geosciences.
