CONVERGENCE OF THE ONE-DIMENSIONAL CAHN-HILLIARD EQUATION

被引：15

作者：

Bellettini, Giovanni ^{[1
]}

Bertini, Lorenzo ^{[2
]}

Mariani, Mauro ^{[3
]}

Novaga, Matteo ^{[4
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[3] Univ Aix Marseille, Lab Anal, Topol Probabil UMR 6632, CNRS, F-13397 Marseille 20, France

[4] Univ Padua, Dipartimento Matemat, I-35121 Padua, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2012年 / 44卷 / 05期

关键词：

Cahn-Hilliard equation; Gamma-convergence; forward-backward equations; GAMMA-CONVERGENCE; GRADIENT FLOWS; DYNAMICS; LIMIT;

D O I：

10.1137/120865410

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cahn-Hilliard equation in one space dimension with scaling parameter epsilon, i.e., u(t) = (W'(u) - epsilon(2)u(xx))(xx), where W is a nonconvex potential. In the limit epsilon down arrow 0, under the assumption that the initial data are energetically well prepared, we show the convergence to a Stefan problem. The proof is based on variational methods and exploits the gradient flow structure of the Cahn-Hilliard equation.

引用

页码：3458 / 3480

页数：23

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