Differential and Integral Equations

On the one-dimensional Ginsburg-Landau {BVP}s

Man Kam Kwong

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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.

Article information

Differential Integral Equations, Volume 8, Number 6 (1995), 1395-1405.

First available in Project Euclid: 15 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 34A47 82D55: Superconductors


Kwong, Man Kam. On the one-dimensional Ginsburg-Landau {BVP}s. Differential Integral Equations 8 (1995), no. 6, 1395--1405. https://projecteuclid.org/euclid.die/1368638173

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