  This article develops a global existence result for the solution of an
optimal control problem associated to the Ginzburg-Landau system. This main
result is based on standard tools of analysis and functional analysis, such as
the Friedrichs Curl Inequality and the Rellich-Kondrashov Theorem. In the
concerning model, we consider the presence of an external magnetic field and
the control variable is a complex function acting on the super-conducting
sample boundary. Finally the state variables are the Ginzburg-Landau order
parameter and the magnetic potential, defined on domains properly specified.
