Analysis and approximation of optimal control problems for a simplified Ginzburg-Landau model of superconductivity (Q1363212)

This paper is concerned with optimal control problems for a Ginzburg-Landau model for superconductivity. The essential analysis is to find the minimum of a functional of the form \[ k_1 \int(\psi_1- \psi)^2d\Omega+ k_2 \int (g^2_1+ g^2_2)d\Gamma, \] where \(\psi\) is the exact solution and boundary conditions are imposed. It is first shown that an optimal solution exists and then Lagrange multipliers are used to enforce the constraints. Numerical examples are given.