O. Chau, M. Shillor and M. Sofonea,

A model for the dynamic, adhesive, frictionless contact between a
viscoelastic body and a deformable foundation is described. The adhesion
process is modeled by a bonding field on the contact surface. The contact is
described by a modified normal compliance condition. 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 a
differential equation for the bonding field. The existence of a unique weak
solution for the problem is established, together with partial regularity result.
The existence proof proceeds by construction of an appropriate mapping which
is shown to be a contraction on a Hilbert space.