L. Jianu, M. Shillor and M. Sofonea,

We consider a model for the quasistatic, bilateral, adhesive and frictionless
contact between a viscoelastic body and a rigid foundation. The adhesion
process on the contact surface is modeled by a surface internal variable, the
bonding field, and the tangential shear due to the bonding field is included.
The problem is formulated as a coupled system of a variational equality for
the displacements and an integro-differential equation for the bonding field.
The existence of a unique weak solution for the problem is established by
construction of an appropriate mapping which is shown to be a contraction
on a Hilbert space. We also consider the problem describing the bilateral contact
between two viscoelastic bodies, and establish similar results.