Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations. (4th December 2017)

• Record Type: Journal Article
• Authors: Beilina, L; Cristofol, M; Li, S; Yamamoto, M
• Is Part Of: Inverse problems. Volume 34:Number 1(2018:Jan.)
• Publication Date: 2017-12-04
• Subjects: coefficient inverse problem -- Carleman estimate -- an acoustic equation of hyperbolic type -- two space-dependent coefficients -- adaptive algorithm; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa941d
• Languages: English
• ISSNs: 0266-5611

Abstract

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.