Applied Mathematics Seminar

Speaker: Junshan Lin

Title: Inverse Source Problems for the Acoustic and Electromagnetic Waves

Abstract:  This talk seeks to give an introduction to "inverse problems." I will focus on the inverse source problem (ISP), which is a typical type of inverse problem for its important practical applications, clear math, and close relations to other inverse scattering problems.

In the first half of the talk, I will give an overview of the ISP and explain in details about the ill-posedness, which is a common issue for most inverse problems, based upon the mathematical structure behind the ISP. This part is intended for graduate students and those who do not have any background in inverse problems. The second half of the talk will consist of more recent developments for this topic. More precisely, I will illustrate how the ill-posedness of the ISP can be alleviated with multiple frequency data or when some a priori information about the source is given. Both the theory and numerics will be covered.