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

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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.