A bilateral contact problem with adhesion and damage between two viscoelastic bodies

This paper deals with the study of a mathematical model which describes the bilateral, frictionless adhesive contact between two viscoelastic bodies with damage. The adhesion of the contact surfaces is con sidered and is modeled with a surface variable, the bonding field, whose evolution is described by a first order differential equation. We establish a variational formulation for the problem and prove the existence and uniqueness result of the solution. The proofs are based on timedependent variational equalities, a classical existence and uniqueness result on parabolic equations, differential equations, and fixedpoint arguments.