讲座主题：Uniqueness of the inverse transmission scattering with a conductive boundary condition
This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number. In the first part of this paper, adequate preparations for the main uniqueness result are made. We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves. Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method. Finally, the a priori estimates of solutions to the general transmission problem with boundary data in With boundary data
are proven by the boundary integral equation method. In the second part of this paper, we give a novel proof on the uniqueness of the inverse conductive scattering problem.