Phase transitions and generalized motion by mean curvature

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

Research output: Contribution to journalArticlepeer-review

399 Scopus citations


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
Issue number9
StatePublished - Oct 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


Dive into the research topics of 'Phase transitions and generalized motion by mean curvature'. Together they form a unique fingerprint.

Cite this