Increasing stability in the two dimensional inverse source scattering problem with attenuation and many frequencies. (22nd August 2018)

• Record Type: Journal Article
• Authors: Entekhabi, Mozhgan Nora
• Is Part Of: Inverse problems. Volume 34:Number 11(2018:Nov.)
• Publication Date: 2018-08-22
• Subjects: inverse source problems -- scattering theory -- exact observability -- Fourier transform; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aad677
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we investigate the interior inverse source problem for the Helmholtz equation with attenuation in the plane from boundary Cauchy data of multiple frequencies when the source term is assumed to be compactly supported in an arbitrary domain Ω with sufficiently smooth boundary. The main goal of this paper is to understand the dependence of increasing stability on the attenuation factor or constant damping. Using Fourier transform with respect to the wave numbers, explicit bounds for the analytic continuation and Hankel function and exact observability and Carleman estimates for the wave equation led us to our goal which is an increasing stability estimates with larger wave numbers interval.