Fourier approach to inverse source problems in the time domain
Abstract: This talk is concerned with inverse time-dependent source problems for the scalar wave equation. A Fourier approach will be presented to show uniqueness and stability for recovering time-depdendent soure terms. The basic idea is to reduce the time-dependent problem to an inverse problem in the Fourier-Laplace domain with multi-frequency data. In particular, we will show uniqueness to inverse moving source problems of recovering source profile and orbit functions. This talk is based on recent joint works with Yavar Kian and Yue Zhao.