  In this paper we contribute to studying the issue of quasistatic limit in the
context of Griffith's theory by investigating a one-dimensional debonding
model. It describes the evolution of a thin film partially glued to a rigid
substrate and subjected to a vertical loading. Taking friction into account and
under suitable assumptions on the toughness of the glue, we prove that, in
contrast to what happens in the undamped case, dynamic solutions converge to
the quasistatic one when inertia and viscosity go to zero, except for a
possible discontinuity at the initial time. We then characterise the size of
the jump by means of an asymptotic analysis of the debonding front.
