Numerical mountain pass solutions of Ginzburg-Landau type equations

Dmitry Glotov; P. J. McKenna

doi:10.3934/cpaa.2008.7.1345

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2008, Volume 7, Issue 6: 1345-1359. Doi: 10.3934/cpaa.2008.7.1345

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Numerical mountain pass solutions of Ginzburg-Landau type equations

Dmitry Glotov^1, and
P. J. McKenna^1,

1.
Department of Mathematics, 196 Auditorium Road, Unit 3009, University of Connecticut, Storrs, CT 06269-3009

Received: July 31, 2007

Revised: April 30, 2008

Published: October 2008

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Abstract

We study the numerical solutions of a system of Ginzburg-Landau type equations arising in the thin film model of superconductivity. These solutions are obtained by the Mountain Pass algorithm that was originally developed for semilinear elliptic equations. We prove a key hypothesis of the Mountain Pass theorem and investigate the physical features of the solutions such as the presence, the number, and the location of vortices and the numerical properties such as stability.

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Mathematics Subject Classification: Primary: 35J60, 35J50; Secondary: 65N99.

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