Recovering the initial condition in the One-Phase Stefan problem
Analysis of PDEs
2021-05-27 v2
Abstract
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary solution. Then we study the uniqueness and stability of the inversion. The principal contribution of the paper is a new logarithmic type stability estimate that shows that the inversion may be severely ill-posed. The proof is based on integral equations representation techniques, and the unique continuation property for parabolic type solutions. We also present few numerical examples operating with noisy synthetic data.
Cite
@article{arxiv.2103.14751,
title = {Recovering the initial condition in the One-Phase Stefan problem},
author = {Chifaa Ghanmi and Saloua Mani Aouadi and Faouzi Triki},
journal= {arXiv preprint arXiv:2103.14751},
year = {2021}
}
Comments
22 pages, 6 figures, 6 tables. arXiv admin note: text overlap with arXiv:2002.09185