Uniqueness of the maximal solution of the supercooled Stefan problem in 1D
Analysis of PDEs
2026-01-05 v1 Probability
Abstract
We prove uniqueness of the maximal weak solutions to the supercooled Stefan problem in 1 dimension. This follows by showing that in 1 dimension, the optimal solution of the corresponding free target optimal transport problem given in \cite{GeneralDimensions}, is independent of the choice of the cost function. Moreover, we show that the supercooled Stefan problem lacks monotonicity and -Lipschitz stability, which are available in a similar problem considered in a previous paper \cite{freetarget}. However, in dimension, it has stability in the weak convergence of measures.
Keywords
Cite
@article{arxiv.2601.00234,
title = {Uniqueness of the maximal solution of the supercooled Stefan problem in 1D},
author = {Kai Hong Chau and Young-Heon Kim and Mathav Murugan},
journal= {arXiv preprint arXiv:2601.00234},
year = {2026}
}