Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
Year: 2026
Type: preprint
Abstract: Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cahn equations. We prove - for the first time - a global, unconditional convergence result for such a coupled system and show that the limit is a multiphase mean curvature flow in the sense of Brakke.
Source: arXiv (Cornell University)
Authors: Laux, Tim, Takasao, Keisuke
Institutions: Heidelberg University, Kyoto University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1620761618, Mathematical analysis on interface motions allowing collision, rupture and coalasce, Measure theoretic properties of phase field models for surface evolution equations, G6526081583, EXC 2181: STRUKTUREN: Emergenz in Natur, Mathematik und komplexen Daten, G7227535049, Canonical mean curvature flow and its application to evolution problems, 自己駆動体運動を記述する反応拡散系モデルとその数理解析
OpenAlex ID: W7204580263