Uniqueness of the maximal solution of the supercooled Stefan problem in 1D
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915703669391360 |
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| author | Chau, Kai Hong Kim, Young-Heon Murugan, Mathav |
| author_facet | Chau, Kai Hong Kim, Young-Heon Murugan, Mathav |
| contents | 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 $L^1$-Lipschitz stability, which are available in a similar problem considered in a previous paper \cite{freetarget}. However, in $1$ dimension, it has stability in the weak convergence of measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00234 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness of the maximal solution of the supercooled Stefan problem in 1D Chau, Kai Hong Kim, Young-Heon Murugan, Mathav Analysis of PDEs Probability 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 $L^1$-Lipschitz stability, which are available in a similar problem considered in a previous paper \cite{freetarget}. However, in $1$ dimension, it has stability in the weak convergence of measures. |
| title | Uniqueness of the maximal solution of the supercooled Stefan problem in 1D |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2601.00234 |