Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows

被引：5

作者：

Portegies, Jacobus W. ^{[1
,2
]}

Peletier, Mark A. ^{[2
,3
]}

机构：

[1] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[2] Tech Univ Eindhoven, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

[3] Tech Univ Eindhoven, Inst Complex Mol Syst, NL-5600 MB Eindhoven, Netherlands

来源：

INTERFACES AND FREE BOUNDARIES | 2010年 / 12卷 / 02期

关键词：

STEFAN PROBLEM; LUBRICATION APPROXIMATION; FORMULATION; EQUATIONS;

D O I：

10.4171/IFB/229

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a gradient-flow framework based on the Wasserstein metric for a parabolic moving-boundary problem that models crystal dissolution and precipitation. In doing so we derive a new weak formulation for this moving-boundary problem and we show that this formulation is well-posed. In addition, we develop a new uniqueness technique based on the framework of gradient flows with respect to the Wasserstein metric. With this uniqueness technique, the Wasserstein framework becomes a complete well-posedness setting for this parabolic moving-boundary problem.

引用

页码：121 / 150

页数：30

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