Ginzburg-Landau vortices: Dynamics, pinning, and hysteresis

Fang Hua Lin, Qiang Du

Research output: Contribution to journalArticlepeer-review


In this paper, we consider three problems related to the mathematical study of vortex phenomena in superconductivity based on the G-L models. First, we study the long-time behavior of the solutions of the time-dependent Ginzburg-Landau equations. Then we describe results concerning the pinning effect of thin regions in a variable thickness thin film. Finally, we prove the existence of vortex-like solutions to the steady state Ginzburg-Landau equations and study the hysteresis phenomenon near the lower critical field.

Original languageEnglish (US)
Pages (from-to)1265-1293
Number of pages29
JournalSIAM Journal on Mathematical Analysis
Issue number6
StatePublished - Nov 1997


  • Ginzburg-Landau equations
  • Hysteresis
  • Long-time behavior
  • Superconductivity
  • Vortex pinning
  • Vortex solution

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics


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