## Abstract

We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies between the equilibrium freezing point and the characteristic invariant temperature throughout the liquid our main theorem shows that, as the kinetic undercooling parameter tends to zero, the free boundary converges to the (possibly irregular) free boundary in the supercooled Stefan problem without kinetic undercooling, whose uniqueness has been recently established in (Delarue, Nadtochiy and Shkolnikov (2019), Ledger and Søjmark (2018)). The key tools in the proof are a Feynman-Kac formula, which expresses the free boundary in the problem with kinetic undercooling through a local time of a reflected process, and a resulting comparison principle for the free boundaries with different kinetic undercooling parameters.

Original language | English (US) |
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Pages (from-to) | 861-871 |

Number of pages | 11 |

Journal | Annales de l'institut Henri Poincare (B) Probability and Statistics |

Volume | 58 |

Issue number | 2 |

DOIs | |

State | Published - May 2022 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Keywords

- Feynman-Kac formula
- Free boundary problems
- Kinetic undercooling
- Local time
- Reflected processes
- Supercooled Stefan problem