Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (6): 1768-1790.

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Convergence of Solutions to Dirichlet Problem of Parabolic Allen-Cahn Equation

Changjian Wang1, Gaofeng Zheng2,*()   

  1. 1School of Mathematics and Statistics, Xinyang Normal University, Henan Xinyang 464000
    2School of Mathematics and Statistics, Key Laboratory of Nonlinear Analysis and Applications (Ministry of Education), Hubei Provincial Key Laboratory of Mathematical Physics, Central China Normal University, Wuhan 430079
  • Received:2025-01-06 Revised:2025-04-25 Online:2025-12-26 Published:2025-11-18
  • Contact: Gaofeng Zheng E-mail:gfzheng@mail.ccnu.edu.cn
  • Supported by:
    NSFC(12271195);NSFC(12401144);NSF of Henan Province(242300421695)

Abstract:

The studies on the convergence of Allen-Cahn equation mainly focus on Neumann boundary value problems, but there are few researches on other related boundary value problems. This paper mainly explores the limit varifold induced by the Dirichlet boundary value problem of the parabolic Allen-Cahn equation when the parameters tend to 0, which is Brakke's mean curvature flow.

Key words: parabolic Allen-Cahn equation, Dirichlet problem, Brakke's mean curvature flow

CLC Number: 

  • O175.23
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