Non-minimizing solutions of the Ginzburg-Landau equation

  • Fabrice Bethuel
  • Haïm Brezis
  • Frédéric Hélein
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 13)

Abstract

Throughout this chapter, we analyze the behavior as \( \varepsilon \to 0 \) of solutions vε of the Ginzburg-Landau equation:
$$ - \Delta {v_\varepsilon } = \frac{1}{{{\varepsilon ^2}}}{v_\varepsilon }\left( {1 - {{\left| {{v_\varepsilon }} \right|}^2}} \right)\quad in G $$
(1)
,
$$ {v_\varepsilon } = g\quad on\,\partial G $$
(2)
.

Keywords

Vortex Hull 

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Fabrice Bethuel
    • 1
  • Haïm Brezis
    • 2
    • 3
  • Frédéric Hélein
    • 4
  1. 1.Laboratoire d’Analyse NumériqueUniversité Paris-SudOrsay CedexFrance
  2. 2.Analyse Numérique Université Pierre et Marie CurieParis Cedex 05France
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA
  4. 4.CMLA, ENS-CachanCachan CedexFrance

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