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

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