Inverse inclusion problem: A stable method to determine disks

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Triki, Faouzi¹  Tsou, Chun-Hsiang¹ 

[1] Univ Grenoble Alpes, Lab Jean Kuntzmann, UMR CNRS 5224, 700 Ave Cent, F-38401 St Martin Dheres, France

关键词: Inverse problems;    Uniqueness;    Inclusion;    Unique continuation;    Disks;    Stability estimates;   

DOI  :  10.1016/j.jde.2020.02.028

来源: Elsevier

【 摘 要 】

In this paper we are interested in the inverse inclusion problem in the plane. We derived Holder stability estimates for the inversion using a general single boundary measurement, and under the assumption that the inclusion has a circular shape. The Wilder power in the stability estimates only depends on the position of the target inclusion and shows that the identification is better when the inclusion is closer to the boundary. We finally proposed a simple minimizing numerical scheme for the recovery of the inclusion. Our numerical results are in good agreement with the obtained Wilder stability estimates. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free