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PreprintarXiv licencearXiv

Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow

  • Tim Laux
  • Keisuke Takasao
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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.

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Cite

BibTeXRIS
BibTeX
@misc{laux2026convergence,
  title = {{Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow}},
  author = {Tim Laux and Keisuke Takasao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.26842},
  eprint = {2608.26842},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26842},
}
RIS
TY  - UNPB
TI  - Convergence of a vector-valued Allen-Cahn system to Brakke's multiphase mean curvature flow
AU  - Tim Laux
AU  - Keisuke Takasao
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.26842
UR  - https://arxiv.org/abs/2608.26842
AB  - 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.
ER  -