  In this work we investigate a phase field model for damage processes in
two-dimensional viscoelastic media with nonhomogeneous Neumann data describing
external boundary forces. In the first part we establish global-in-time
existence, uniqueness, a priori estimates and continuous dependence of strong
solutions on the data. The main difficulty is caused by the irreversibility of
the phase field variable which results in a constrained PDE system. In the last
part we consider an optimal control problem where a cost functional penalizes
maximal deviations from prescribed damage profiles. The goal is to minimize the
cost functional with respect to exterior forces acting on the boundary which
play the role of the control variable in the considered model. To this end, we
prove existence of minimizers and study a family of "local" approximations via
adapted cost functionals.
