Kevin T. Andrews and Meir Shillor

A model for the dynamic evolution of an elastic membrane in adhesive contact
with arigid obstacle is developed and analyzed. The adhesion process is modelled by
a bonding field and the contact by Signorini's condition. The mathematical formulation
is in the form of a coupled system consisting of a hyperbolic variational inequality for the
displacement and a first order variational inequality for the bonding field. The hyperbolic
variational inequality involves a unilateral constraint on the displacement. The model
allows for cycles of bonding and rebonding to occur. Existence of a weak solution
is established using penalization and a fixed point argument.