期刊
INDIANA UNIVERSITY MATHEMATICS JOURNAL
卷 66, 期 6, 页码 2015-2035出版社
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2017.66.6183
关键词
Mean curvature flow; Allen-Cahn equation; phase field method
类别
资金
- JSPS KAKENHI [JP16K17622, JP17J02386]
- JSPS
We study the phase field method for the volume-preserving mean curvature flow. Given an initial data which is a measure-theoretic boundary of a Caccioppoli set with a suitable density bound, we prove the existence of the weak solution for the volume-preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula for the reaction diffusion equation.
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