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

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