Recovery of singularities in a fourth-order operator on the line from limited data. (3rd May 2016)

• Record Type: Journal Article
• Authors: Tyni, Teemu; Harju, Markus; Serov, Valery
• Is Part Of: Inverse problems. Volume 32:Number 7(2016:Jul.)
• Publication Date: 2016-05-03
• Subjects: inverse scattering -- Born approximation -- reconstruction of singularities; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/7/075001
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider a differential operator of order four with three coefficients which may be complex valued. We prove that the Born approximation can be used efficiently to recover essential information about a combination of the coefficients from the knowledge of the reflection coefficient. Numerical examples illustrate the feasibility of this method.