Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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 | References | Similar Articles | Additional Information

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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DOI: https://doi.org/10.1090/qam/1359498
Article copyright: © Copyright 1995 American Mathematical Society


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