Phase transitions and generalized motion by mean curvature
L. C. Evans, Halil Mete Soner, Panagiotis E. Souganidis · Communications on Pure and Applied Mathematics · 1992
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.