LOCAL MINIMIZERS AND SLOW MOTION FOR THE MASS PRESERVING ALLEN-CAHN EQUATION IN HIGHER DIMENSIONS

被引：1
|
作者：
Leoni, Giovanni [1 ]
Murray, Ryan [2 ]
机构：
[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
[2] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 12期
关键词：
Second-order Gamma-convergence; rearrangement; Cahn-Hilliard functional; slow motion; Allen-Cahn equation; Cah-Hilliard equation; PHASE-TRANSITIONS; ASYMPTOTIC DEVELOPMENT; BOUNDARY MOTION; GRADIENT THEORY; REGULARITY; PERIMETER;
D O I：
10.1090/proc/13988
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper completely resolves the asymptotic development of order 2 by Gamma-convergence of the mass-constrained Cahn-Hilliard functional. Important new results on the slow motion of interfaces for the mass preserving Allen-Cahn equation and the Cahn-Hilliard equations in higher dimension are obtained as an application.
引用
收藏
页码：5167 / 5182
页数：16
相关论文
共 50 条
  • [1] Slow motion for the nonlocal Allen-Cahn equation in n dimensions
    Murray, Ryan
    Rinaldi, Matteo
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (06)
  • [2] Slow motion for the nonlocal Allen–Cahn equation in n dimensions
    Ryan Murray
    Matteo Rinaldi
    Calculus of Variations and Partial Differential Equations, 2016, 55
  • [3] The Allen-Cahn action functional in higher dimensions
    Mugnai, Luca
    Roeger, Matthias
    INTERFACES AND FREE BOUNDARIES, 2008, 10 (01) : 45 - 78
  • [4] Global minimizers of the Allen-Cahn equation in dimension n ≥ 8
    Liu, Yong
    Wang, Kelei
    Wei, Juncheng
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2017, 108 (06): : 818 - 840
  • [5] MOTION OF A DROPLET FOR THE STOCHASTIC MASS-CONSERVING ALLEN-CAHN EQUATION
    Antonopoulou, D. C.
    Bates, P. W.
    Bloemker, D.
    Karali, G. D.
    SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (01) : 670 - 708
  • [6] Slow motion for a hyperbolic variation of Allen-Cahn equation in one space dimension
    Folino, Raffaele
    JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2017, 14 (01) : 1 - 26
  • [7] Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
    Chen, Xinfu
    Hilhorst, D.
    Logak, E.
    INTERFACES AND FREE BOUNDARIES, 2010, 12 (04) : 527 - 549
  • [8] MOTION OF INTERFACES FOR A DAMPED HYPERBOLIC ALLEN-CAHN EQUATION
    Folino, Raffaele
    Lattanzio, Corrado
    Mascia, Corrado
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (09) : 4507 - 4543
  • [9] A stable and structure-preserving scheme for a non-local Allen-Cahn equation
    Okumura, Makoto
    JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2018, 35 (03) : 1245 - 1281
  • [10] ON THE MAXIMUM PRINCIPLE PRESERVING SCHEMES FOR THE GENERALIZED ALLEN-CAHN EQUATION
    Shen, Jie
    Tang, Tao
    Yang, Jiang
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2016, 14 (06) : 1517 - 1534
12345