GAMMA CONVERGENCE FOR THE DE GENNES-CAHN-HILLIARD ENERGY

被引：0

作者：

Dai, Shibin ^{[1
]}

Renzi, Joseph ^{[1
]}

Wise, Steven M. ^{[2
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Univ Tennessee, Dept Math, 227 Ayres Hall 1403 Circle Dr, Knoxville, TN 37996 USA

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2023年 / 21卷 / 08期

基金：

美国国家科学基金会;

关键词：

de Gennes-Cahn-Hilliard energy; Gamma convergence; sharp interface limit; surface diffusion; PHASE-FIELD MODEL; FINITE-ELEMENT-METHOD; SURFACE-DIFFUSION; DISCRETE SCHEME; EQUATION; EVOLUTION; MOTION; FILMS; SHARP; LAWS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The degenerate de Gennes-Cahn-Hilliard (dGCH) equation is a model for phase separation which may more closely approximate surface diffusion than others in the limit when the thickness of the transition layer approaches zero. As a first step to understand the limiting behavior, in this paper we study the Gamma-limit of the dGCH energy. We find that its Gamma-limit is a constant multiple of the interface area, where the constant is determined by the de Gennes coefficient together with the double well potential. In contrast, the transition layer profile is solely determined by the double well potential.

引用

页码：2131 / 2144

页数：14

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