On the minimizers of the Ginzburg-Landau energy for high kappa: the one-dimensional case

The Ginzburg-Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg-Landau parameter kappa formally equal to infinity, the existence of a minimizer of this reduced Ginzburg-Landau energy is proved. Then asymptotic behaviour for large kappa of minimizers of the full Ginzburg-Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.