  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.
