Optimal control of dynamical Ginzburg-Landau vortices in superconductivity

In this paper we consider an optimal control problem which is governed by a generalized Ginzburg-Landau model which describes the phase transitions taking place in the superconducting films with variable thickness. The objective of the work is to explore the possibilities of controlling the motion of vortices in the superconducting films through the external magnetic field. The existence of solutions of the nonlinear governing system of equations is established by a rigorous analysis of the method of lines. The existence of optimal solutions and the first order necessary conditions for optimality are obtained.