Singular limit of an Allen-Cahn equation with nonlinear diffusion

被引：1

作者：

El Kettani, Perla ^{[1
]}

Funaki, Tadahisa ^{[2
,3
]}

Hilhorst, Danielle ^{[4
,5
]}

Park, Hyunjoon ^{[6
]}

Sethuraman, Sunder ^{[7
]}

机构：

[1] Univ Toulon & Var, Toulon, France

[2] Univ Tokyo, Grad Sch Math Sci, Dept Math, Tokyo, Japan

[3] Waseda Univ, Dept Math, Tokyo, Japan

[4] Paris Saclay Univ, CNRS, Orsay, France

[5] Paris Saclay Univ, Lab Math, Orsay, France

[6] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon, South Korea

[7] Univ Arizona, Dept Math, Tucson, AZ USA

来源：

TUNISIAN JOURNAL OF MATHEMATICS | 2022年 / 4卷 / 04期

关键词：

Allen-Cahn equation; mean curvature flow; singular limit; nonlinear diffusion; interface; surface tension; MOTION; GENERATION; INTERFACE;

D O I：

10.2140/tunis.2022.4.719

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an Allen-Cahn equation with nonlinear diffusion, motivated by the study of the scaling limit of certain interacting particle systems. We investigate its singular limit and show the generation and propagation of an interface in the limit. The evolution of this limit interface is governed by mean curvature flow with a novel, homogenized speed in terms of a surface tension-mobility parameter emerging from the nonlinearity in our equation.

引用

页码：719 / 754

页数：37

共 50 条

[31] OPTIMAL CONTROL OF AN ALLEN-CAHN EQUATION WITH SINGULAR POTENTIALS AND DYNAMIC BOUNDARY CONDITION
Colli, Pierluigi
Sprekels, Juergen
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (01) : 213 - 234
[32] Differential Harnack Estimates for a Nonlinear Evolution Equation of Allen-Cahn Type
Abolarinwa, Abimbola
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2021, 18 (05)
[33] NONLINEAR STABILITY OF THE IMPLICIT-EXPLICIT METHODS FOR THE ALLEN-CAHN EQUATION
Feng, Xinlong
Song, Huailing
Tang, Tao
Yang, Jiang
INVERSE PROBLEMS AND IMAGING, 2013, 7 (03) : 679 - 695
[34] THE ALLEN-CAHN EQUATION WITH NONLINEAR TRUNCATED LAPLACIANS: DESCRIPTION OF RADIAL SOLUTIONS
Alfaro, Matthieu
Jouan, Philippe
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2025, 45 (06) : 1891 - 1910
[35] NUMERICAL STUDIES OF DISCRETE APPROXIMATIONS TO THE ALLEN-CAHN EQUATION IN THE SHARP INTERFACE LIMIT
Zhang, Jian
Du, Qiang
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2009, 31 (04): : 3042 - 3063
[36] SHARP INTERFACE LIMIT FOR STOCHASTICALLY PERTURBED MASS CONSERVING ALLEN-CAHN EQUATION
Funaki, Tadahisa
Yokoyama, Satoshi
ANNALS OF PROBABILITY, 2019, 47 (01): : 560 - 612
[37] On an anisotropic doubly nonlinear Allen–Cahn equation with singular potentials
Ahmad Makki
Alain Miranville
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018, 112 : 37 - 55
[38] On a Cahn-Hilliard/Allen-Cahn system coupled with a type III heat equation and singular potentials
Makki, Ahmad
Miranville, Alain
Saoud, Wafa
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 196
[39] Malliavin calculus for the stochastic Cahn-Hilliard/Allen-Cahn equation with unbounded noise diffusion
Antonopoulou, Dimitra C.
Farazakis, Dimitris
Karali, Georgia
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (07) : 3168 - 3211
[40] Global Dynamics of the Cahn-Hilliard/Allen-Cahn Equation
Ma, Mingze
Zhao, Xiaopeng
JOURNAL OF MATHEMATICAL STUDY, 2023, 56 (02) : 156 - 172

← 1 2 3 4 5 →