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
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
收藏
页码:121 / 150
页数:30
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