Always-Scattering, Non-Scattering, and Inverse Scattering

Jingni Xiao (Drexel University, USA)

In this talk, I will present some recent progress on always-scattering, non- scattering, and their connections to inverse scattering.
We consider scattering problems when a medium is probed by incident waves and as a result scattered waves are induced. The aim of inverse scattering is to deduce information about an unknown medium by measuring the corre- sponding scattered waves outside the medium. Inverse scattering has appli- cations in many fields of science and technology, of which radar is one of the most prevalent.
Non-scattering is a particular phenomenon that arises when a medium is probed but no scattered waves can be measured externally. Non-scattering impacts inverse scattering, and it has applications in invisibility where one tries to avoid detection of an object. Moreover, non-scattering is related to resonance, injectivity of the relative scattering operator, and free bound- ary problems. There can be situations when non-scattering never occurs for a given medium; this phenomenon is called always-scattering. The always- scattering feature has applications in inverse problems for uniquely determin- ing the shape or other properties of a medium from scattering measurements.