  In this paper we analyse a one-dimensional debonding model for a thin film
peeled from a substrate when viscosity is taken into account. It is described
by the weakly damped wave equation whose domain, the debonded region, grows
according to a Griffith's criterion. Firstly we prove that the equation admits
a unique solution when the evolution of the debonding front is assigned.
Finally we provide an existence and uniqueness result for the coupled problem
given by the wave equation together with Griffith's criterion.
