Identification of a boundary influx condition in a one-phase Stefan problem. Issue 18 (12th December 2022)

• Record Type: Journal Article
• Authors: Ghanmi, Chifaa; Mani Aouadi, Saloua; Triki, Faouzi
• Is Part Of: Applicable analysis. Volume 101:Issue 18(2022)
• Page Start: 6573
• Page End: 6595
• Publication Date: 2022-12-12
• Subjects: Inverse problem -- stability estimates -- free boundary -- Stefan problem; 35R30 -- 35R35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1934456
• Languages: English
• ISSNs: 0003-6811

Abstract

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 may be severely ill-posed. The proof is based on integral equations and unique continuation of 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.