An integrodifferential model for phase transitions: Stationary solutions in higher space dimensions

被引：162
作者：
Bates, PW [1 ]
Chmaj, A [1 ]
机构：
[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA
来源：
JOURNAL OF STATISTICAL PHYSICS | 1999年 / 95卷 / 5-6期
关键词：
nonlocal Allen-Cahn equation; long-range interaction; pinning;
D O I：
10.1023/A:1004514803625
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study the existence and stability of stationary solutions of an integrodifferential model for phase transitions, which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity. As such, this model is a nonlocal extension of the Allen-Cahn equation, which incorporates long-range interactions. We find that the set of stationary solutions for this model is much larger than that of the Allen-Cahn equation.
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页码：1119 / 1139
页数：21
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