Well-posedness and long-time behaviour for a model of contact with adhesion

This paper addresses the analysis of a model, proposed by M. Frémond, for the phenomenon of contact with reversible adhesion between a viscoelastic body and a rigid support. First of all, we prove existence and uniqueness of global-in-time solutions of (the initial-boundary value problem for) the related PDE system by means of a fixed point technique. Hence, we investigate the long-time behaviour of such solutions and obtain some results on the structure of the associated ω-limit set.