Asymptotic analysis of the Ginzburg-Landau model of superconductivity: reduction to a free boundary model

Author:
S. J. Chapman

Journal:
Quart. Appl. Math. **53** (1995), 601-627

MSC:
Primary 82D55; Secondary 35C20, 35Q55, 80A22

DOI:
https://doi.org/10.1090/qam/1359498

MathSciNet review:
MR1359498

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Abstract: 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.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1359498

Article copyright:
© Copyright 1995
American Mathematical Society