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 language | English (US) |
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Pages (from-to) | 1097-1123 |
Number of pages | 27 |
Journal | Communications on Pure and Applied Mathematics |
Volume | 45 |
Issue number | 9 |
DOIs | |
State | Published - Oct 1992 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics