Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

Impact Factor:2.1

DOI number:10.1088/1361-6420/aa941d

Journal:Inverse Problems

Key Words:coefficient inverse problem; Carleman estimate; an acoustic equation of hyperbolic type; two space-dependent coefficients; adaptive algorithm

Abstract:We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data.

Co-author:L Beilina,M Cristofol,S Li,M Yamamoto

Indexed by:Journal paper

Document Code:000428757900001

Discipline:Natural Science

Document Type:J

Volume:34

Issue:1

Page Number:015001

ISSN No.:0266-5611

Translation or Not:no

Date of Publication:2018-01-01

Included Journals:SCI、EI

Links to published journals:https://iopscience.iop.org/article/10.1088/1361-6420/aa941d