Existence of long-time solutions to dynamic problems of viscoelasticity with rate-and-state friction

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.