Asymptotic Analysis of the Ginzburg-Landau Model of Superconductivity : Reduction to a Free Boundary Model

S. J. Chapman

A detailed formal asymptotic analysis of the Ginzburg-Landau model of superconductivity is performed and it is found that the leading order solution satisfies a vectorial version of the Stefan problem for the melting or solidification of a pure material. The first order correction to this solution is found to contain terms analogous to those of surface tension and kinetic undercooling in the scalar Stefan model. However, the ``surface energy'' of a superconducting material is found to take both positive and negative values, defining type I and type II superconductors respectively, leading to the conclusion that the free boundary model is only appropriate for type I superconductors.