Geodesic
Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows
Jacobus W. Portegies1 ; Mark A. Peletier2
1New York University, USA
2Eindhoven University of Technology, Netherlands
Interfaces and free boundaries, Tome 12 (2010) no. 2, pp. 121-150

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DOI

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.
DOI : 10.4171/ifb/229
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Jacobus W. Portegies  1   ; Mark A. Peletier  2

1 New York University, USA
2 Eindhoven University of Technology, Netherlands 
Jacobus W. Portegies; Mark A. Peletier. Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows. Interfaces and free boundaries, Tome 12 (2010) no. 2, pp. 121-150. doi: 10.4171/ifb/229
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     title = {Well-posedness of a parabolic moving-boundary problem in the setting of {Wasserstein} gradient flows},
     journal = {Interfaces and free boundaries},
     pages = {121--150},
     year = {2010},
     volume = {12},
     number = {2},
     doi = {10.4171/ifb/229},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/229/}
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