On increasing stability in the two dimensional inverse source scattering problem with many frequencies. (29th March 2018)

• Record Type: Journal Article
• Authors: Entekhabi, Mozhgan Nora; Isakov, Victor
• Is Part Of: Inverse problems. Volume 34:Number 5(2018:May)
• Publication Date: 2018-03-29
• Subjects: inverse scattering problems -- inverse source problems -- analytic continuation -- boundary control; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aab465
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.