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1995 On the one-dimensional Ginsburg-Landau {BVP}s
Man Kam Kwong
Differential Integral Equations 8(6): 1395-1405 (1995).


We study the one-dimensional system of Ginzburg-Landau equations that models a thin film of superconductor subjected to a tangential magnetic field. We prove that the bifurcation curve for the symmetric problem is the graph of a continuous function of the supremum of the order parameter. We also prove the existence of a critical magnetic field. In general, there is more than one positive solution to the symmetric boundary value problem. Our numerical experiments have shown cases with three solutions. It is still an open question whether only one of these corresponds to the physical solution that minimizes the Gibbs free energy. We establish uniqueness for a related boundary value problem.


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Man Kam Kwong. "On the one-dimensional Ginsburg-Landau {BVP}s." Differential Integral Equations 8 (6) 1395 - 1405, 1995.


Published: 1995
First available in Project Euclid: 15 May 2013

zbMATH: 0841.34018
MathSciNet: MR1329848

Primary: 34B15
Secondary: 34A47 , 82D55

Rights: Copyright © 1995 Khayyam Publishing, Inc.


Vol.8 • No. 6 • 1995
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