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Radially symmetric solutions for a limiting form of the Ginzburg—Landau model

Published online by Cambridge University Press:  30 January 2013

Xingfei Xiang
Xingfei Xiang*
Affiliation:
Department of Mathematics, East China Normal University, Shanghai 200241, People's Republic of China (xiangxingfei@126.com)
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Abstract

We obtain a solution, the L∞-norm of which is greater than ⅓√3, to the semilinear system arising in the mathematical theory of superconductivity when the domain is a disc or the exterior of a disc in ℝ2. We obtain an estimate of the critical field for the arbitrary penetration depth and determine the critical field as the penetration depth goes to zero when the domain is a disc. We prove that the L∞-norm of the symmetric solutions on the inner boundary is greater than that of the outer boundary when the domain Ω is an annulus. Stability of the solutions is also studied.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 1 , February 2013 , pp. 185 - 203
Copyright
Copyright © Royal Society of Edinburgh 2013

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