The vanishing latent heat limit of a stochastic Stefan problem : An error estimate
Abstract
The purpose of this paper is to extend an article by Hilhorst, Mimura and Schätzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the corresponding stochastic Stefan problem as the latent heat coefficient vanishes. We first prove the existence and uniqueness of the weak solution of this problem, and then study the limit of the solution as the latent heat coefficient tends to zero. Unlike in [18], our method of proof is based upon an error estimate between the solution of the Stefan problem with positive latent heat and that of the Stefan problem with zero latent heat, which seems to be novel even in the deterministic case when no noise is added.
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BibTeX
@misc{ciotir2026vanishing,
title = {{The vanishing latent heat limit of a stochastic Stefan problem : An error estimate}},
author = {Ioana Ciotir and Perla El Kettani and Dan Goreac and Danielle Hilhorst},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17079},
eprint = {2609.17079},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05740263v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The vanishing latent heat limit of a stochastic Stefan problem : An error estimate
AU - Ioana Ciotir
AU - Perla El Kettani
AU - Dan Goreac
AU - Danielle Hilhorst
PY - 2026
DA - 2026/09/07
PB - HAL
DO - 10.48550/arxiv.2609.17079
UR - https://hal.science/hal-05740263v1
AB - The purpose of this paper is to extend an article by Hilhorst, Mimura and Schätzle [18] about the limit as the latent heat coefficient tends to zero of a two-phase Stefan problem arising in biology. We introduce a rather general additive noise white in time and colored in space, and search for the limit of the solution of the corresponding stochastic Stefan problem as the latent heat coefficient vanishes. We first prove the existence and uniqueness of the weak solution of this problem, and then study the limit of the solution as the latent heat coefficient tends to zero. Unlike in [18], our method of proof is based upon an error estimate between the solution of the Stefan problem with positive latent heat and that of the Stefan problem with zero latent heat, which seems to be novel even in the deterministic case when no noise is added.
ER -