Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Thursday, Jan 6, 2022
Time: 4:00PM
Location: JWB 335
Jingni Xiao
Rutgers University
Title |
Scattering, Nonscattering, and Inverse Scattering |
Abstract |
Scattering studies the response of a known medium when probed with waves. In inverse scattering one seeks for information of an unknown medium from the exterior measurement of the scattered waves. One of the interesting questions in both scattering and inverse scattering is whether the scattering response could be zero in the exterior when a medium is probed by certain waves. I plan to describe some results concerning this question in two different cases. The first is when the medium has corner(s) in its shape, for which we show that corners “almost” always scatter, with some exceptions. We also apply this result in inverse scattering. The other is when a medium has smooth boundary, in which case we prove the finiteness of nonscattering wavenumbers. This question is also related to invisibility, Schiffer’s conjecture (and Pompeiu’s problem), as well as free boundary problems. |
Computational Mathematics
Applied Mathematics