A contact problem for a plate and a beam in presence of adhesion

Under consideration is the problem of contact between a plate and a beam. It is assumed that no mutual penetration between the plate and the beam can occur, and so an appropriate nonpenetration condition is used. On the other hand, the adhesion of the bodies is taken into account which is characterized by a numerical adhesion parameter. We study the existence and uniqueness of a solution for the contact problem as well as the passage to the limit with respect to the adhesion parameter. The accompanying optimal control problem is investigated in which the adhesion parameter acts as a control parameter.