On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes

Leonid V. Berlyand, Dmitry Golovaty, Oleksandr Iaroshenko, Volodymyr Rybalko

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider a two-dimensional Ginzburg–Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg–Landau parameter vs. hole radius) is motivated by a recently discovered phenomenon of vortex phase separation in superconducting composites. We show that, for each hole, the degrees of minimizers of the Ginzburg–Landau problems in the classes of S1-valued and C-valued maps, respectively, are the same. The presence of two parameters that are widely separated on a logarithmic scale constitutes the principal difficulty of the analysis that is based on energy decomposition techniques.

Original languageEnglish (US)
Pages (from-to)1317-1347
Number of pages31
JournalJournal of Differential Equations
Volume264
Issue number2
DOIs
StatePublished - Jan 15 2018

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Minimizer
Phase separation
Vortex flow
Decomposition
Composite materials
Approximation
Scaling Relations
Decomposition Techniques
Phase Separation
Two Parameters
Vortex
Logarithmic
Radius
Composite
Arbitrary
Energy

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Berlyand, Leonid V. ; Golovaty, Dmitry ; Iaroshenko, Oleksandr ; Rybalko, Volodymyr. / On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes. In: Journal of Differential Equations. 2018 ; Vol. 264, No. 2. pp. 1317-1347.
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On approximation of Ginzburg–Landau minimizers by S1-valued maps in domains with vanishingly small holes. / Berlyand, Leonid V.; Golovaty, Dmitry; Iaroshenko, Oleksandr; Rybalko, Volodymyr.

In: Journal of Differential Equations, Vol. 264, No. 2, 15.01.2018, p. 1317-1347.

Research output: Contribution to journalArticle

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