  We consider an optimal control problem subject to the thin-film equation
which is deduced from the Navier--Stokes equation. The PDE constraint lacks
well-posedness for general right-hand sides due to possible degeneracies; state
constraints are used to circumvent this problematic issue and to ensure
well-posedness, and the rigorous derivation of necessary optimality conditions
for the optimal control problem is performed. A multi-parameter regularization
is considered which addresses both, the possibly degenerate term in the
equation and the state constraint, and convergence is shown for vanishing
regularization parameters by decoupling both effects. The fully regularized
optimal control problem allows for practical simulations which are provided,
including the control of a dewetting scenario, to evidence the need of the
state constraint, and to motivate proper scalings of involved regularization
and numerical parameters.
