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

TL;DR

This paper establishes a well-posed Wasserstein gradient flow framework for a parabolic moving-boundary problem modeling crystal dissolution and precipitation, introducing new formulations and a uniqueness technique.

Contribution

It develops a novel weak formulation and a new uniqueness method within the Wasserstein gradient flow framework for moving-boundary problems.

Findings

The weak formulation is well-posed.

A new uniqueness technique is introduced.

The framework ensures complete well-posedness.

Abstract

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.