Identification of a boundary influx condition in a one-phase Stefan problem
Analysis of PDEs
2020-02-24 v1
Abstract
We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a logarithmic stability estimate that shows that the inversion is ill-posed. The proof is based on integral equations and unique continuation for holomorphic functions. We also proposed a direct algorithm with a regularization term to solve the nonlinear inverse problem. Several numerical tests using noisy data are provided with relative errors analysis.
Cite
@article{arxiv.2002.09185,
title = {Identification of a boundary influx condition in a one-phase Stefan problem},
author = {Chifaa Ghanmi and Saloua Mani-Aouadi and Faouzi Triki},
journal= {arXiv preprint arXiv:2002.09185},
year = {2020}
}