Increasing stability in the two dimensional inverse source scattering problem with attenuation and many frequencies

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 Omega 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 Cadman estimates for the wave equation led us to our goal which is an increasing stability estimates with larger wave numbers interval.