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

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