In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction 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.

Models with a multiplet of field variables arranged into rectangular matrices, in the limit of infinite dimensions of the matrices, are studied. In zero-dimensional space (where the problem is a combinatorial one) a closed solution is given that improves the one previously known. In arbitrary space dimension a symmetry is described that connects rectangular models with vector models.

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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.

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