We study the interior inverse source problem for the Helmholtz equation from boundary Cauchy data of multiple wave numbers. The main goal of this paper is to understand the dependence of increasing stability on the attenuation, both analytically and numerically. To implement it we use the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, and observability bounds for the wave equation. In particular, by using Carleman estimates for the wave equation we trace the dependence of exact observability bounds on the constant damping. Numerical examples in 3 spatial dimension support the theoretical results. It is a joint work with Prof. Victor Isakov (Wichita State University).

Shuai Lu received the B.S. and M.S. degrees from Fudan University (China) in 2001 and 2004, respectively, and the Ph.D. degree (with distinction) from Johannes Kepler University of Linz (Austria), in 2007. From 2007 to 2010, he was a Postdoctoral Fellow with the Austrian Academy of Sciences. In 2010, he joined the School of Mathematical Sciences, Fudan University, where he became a Full Professor in 2015. From 2011 to 2012, he was a Humboldt Research Fellow for Postdoctoral researchers with the Weierstrass Institute for Applied Analysis and Stochastics in Berlin, Germany. He has authored or co-authored over 43 SCI papers in peer-reviewed journals and one monograph. His research interests include inverse problems, from both deterministic and stochastic viewpoints.