PreprintCC BY 4.0arXiv
A transform approach to the supercooled Stefan problem
Abstract
We consider a generalisation of the probabilistic reformulation of the supercooled Stefan problem from arXiv:1902.05174 allowing for non-integrable initial data. From an application of Ito's formula, we obtain a relationship between the Laplace transform of the initial data and a transform of the solution, together with its possibly discontinuous free boundary. Using this relationship we give a sharp existence result for global solutions, we extend previous results on the uniqueness of solutions, and we determine the asymptotic behaviour of solutions for a certain class of initial data.
Versions
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BibTeX
@misc{blore2026transform,
title = {{A transform approach to the supercooled Stefan problem}},
author = {Thomas Blore and Ben Hambly},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24297},
eprint = {2609.24297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24297},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A transform approach to the supercooled Stefan problem
AU - Thomas Blore
AU - Ben Hambly
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24297
UR - https://arxiv.org/abs/2609.24297
AB - We consider a generalisation of the probabilistic reformulation of the supercooled Stefan problem from arXiv:1902.05174 allowing for non-integrable initial data. From an application of Ito's formula, we obtain a relationship between the Laplace transform of the initial data and a transform of the solution, together with its possibly discontinuous free boundary. Using this relationship we give a sharp existence result for global solutions, we extend previous results on the uniqueness of solutions, and we determine the asymptotic behaviour of solutions for a certain class of initial data.
ER -