Phase transitions and generalized motion by mean curvature

L. C. Evans, H. M. Soner, P. E. Souganidis

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337 Scopus citations

Abstract

We study the limiting behavior of solutions to appropriately rescaled versions of the Allen‐Cahn equation, a simplified model for dynamic phase transitions. We rigorously establish the existence in the limit of a phase‐antiphase interface evolving according to mean curvature motion. This assertion is valid for all positive time, the motion interpreted in the generalized sense of Evans‐Spruck and Chen‐Giga‐Goto after the onset of geometric singularities.

Original languageEnglish (US)
Pages (from-to)1097-1123
Number of pages27
JournalCommunications on Pure and Applied Mathematics
Volume45
Issue number9
DOIs
StatePublished - Oct 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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