  We investigate a distributed optimal control problem for a nonlocal phase
field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal
version of a model for two-species phase segregation on an atomic lattice under
the presence of diffusion that has been studied in a series of papers by P.
Podio-Guidugli and the present authors. The model consists of a highly
nonlinear parabolic equation coupled to an ordinary differential equation. The
latter equation contains both nonlocal and singular terms that render the
analysis difficult. Standard arguments of optimal control theory do not apply
directly, although the control constraints and the cost functional are of
standard type. We show that the problem admits a solution, and we derive the
first-order necessary conditions of optimality.
