Inverse Source Problem with Many Frequencies and Attenuation for One-Dimensional Domain

In this article, we consider the one-dimensional inverse source problem for Helmholtz equation with attenuation (damping) factor in a one layer medium. We establish a stability by using multiple frequencies at the two end points of the domain which contains the compact support of the source functions. The main result is an estimate which consists of two parts: the data discrepancy and the high frequency tail. We show that increasing stability possible using multi-frequency wave at the two endpoints