  In this paper we address the analytical investigation of a model for adhesive
contact, which includes nonlocal sources of damage on the contact surface, such
as the elongation. The resulting PDE system features various nonlinearities
rendering the unilateral contact conditions, the physical constraints on the
internal variables, as well as the integral contributions related to the
nonlocal forces. For the associated initial-boundary value problem we obtain a
global-in-time existence result by proving the existence of a local solution
via a suitable approximation procedure and then by extending the local solution
to a global one by a nonstandard prolongation argument.
