The transmission eigenvalue and the inverse parameter and shape problems with two conductivity parameters

In this talk, we will study the acoustic direct and inverse scattering problem dealing with two conductivity conditions. First, we analyze the scattering problem from the perspective of transmission eigenvalues (TE) and show how the TE’s depend on the physical parameters of the system. Motivated by the work on TE’s, we focus on recovering the physical parameters of the problem at a fixed incident direction for multiple frequencies. Finally,  we apply qualitative reconstruction methods to recover the scatterer based on measured far-field data, using full aperture in both two and three dimensions, and partial aperture in two dimensions.