Ginzburg-Landau equation and motion by mean curvature, II: Development of the initial interface

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Abstract

In this paper, we study the short time behavior of the solutions of a sequence of Ginzburg-Landau equations indexed by ε. We prove that under appropriate assumptions on the initial data, solutions converge to ±1 in short time and behave like the one-dimensional traveling wave across the interface. In particular, energy remains uniformly bounded in ε.

Original languageEnglish (US)
Pages (from-to)477-491
Number of pages15
JournalJournal of Geometric Analysis
Volume7
Issue number3
DOIs
StatePublished - Jan 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • Ginzburg-Landau equation
  • Maximum principle
  • Traveling waves

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