Diffusion in Allen-Cahn equation: Normal vs anomalous

被引：5
|
作者：
Fan, Enyu [1 ]
Li, Changpin [1 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2024年 / 457卷
基金：
中国国家自然科学基金;
关键词：
Allen-Cahn equation; Fractional derivative; L1; formula; LOGARITHMIC CREEP LAW; SCHEME;
D O I：
10.1016/j.physd.2023.133973
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is known that the anomalous diffusion can be well characterized by the fractional derivatives. In this paper, the Allen-Cahn equations with different kinds of time fractional derivatives are numerically studied. The numerical solutions of the Allen-Cahn equations are obtained by using Euler method or L1 method to approximate the time derivative and the finite element method in the space direction. Finally, the influences of time derivatives on the solutions of the considered models are observed and discussed.
引用
收藏
页数：15
相关论文
共 50 条
  • [21] Some entire solutions of the Allen-Cahn equation
    Fukao, Y
    Morita, Y
    Ninomiya, H
    TAIWANESE JOURNAL OF MATHEMATICS, 2004, 8 (01): : 15 - 32
  • [22] Symmetry of Entire Solutions to the Allen-Cahn Equation
    Gui, Changfeng
    Zhang, Fang
    ADVANCED NONLINEAR STUDIES, 2015, 15 (03) : 587 - 612
  • [23] The fractional Allen-Cahn equation with the sextic potential
    Lee, Seunggyu
    Lee, Dongsun
    APPLIED MATHEMATICS AND COMPUTATION, 2019, 351 : 176 - 192
  • [24] On the discretisation in time of the stochastic Allen-Cahn equation
    Kovacs, Mihaly
    Larsson, Stig
    Lindgren, Fredrik
    MATHEMATISCHE NACHRICHTEN, 2018, 291 (5-6) : 966 - 995
  • [25] Interior layers for an inhomogeneous Allen-Cahn equation
    Du, Zhuoran
    Gui, Changfeng
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (02) : 215 - 239
  • [26] A hybrid FEM for solving the Allen-Cahn equation
    Shin, Jaemin
    Park, Seong-Kwan
    Kim, Junseok
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 244 : 606 - 612
  • [27] Stochastic Allen-Cahn equation with logarithmic potential
    Bertacco, Federico
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 202
  • [28] The hyperbolic Allen-Cahn equation: exact solutions
    Nizovtseva, I. G.
    Galenko, P. K.
    Alexandrov, D. V.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (43)
  • [29] Transition layer for the heterogeneous Allen-Cahn equation
    Mahmoudi, Fethi
    Malchiodi, Andrea
    Wei, Juncheng
    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2008, 25 (03): : 609 - 631
  • [30] Metastable speeds in the fractional Allen-Cahn equation
    Achleitner, Franz
    Kuehn, Christian
    Melenk, Jens M.
    Rieder, Alexander
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 408
12345