The fixed angle scattering problem

Abstract: We first discuss our (with Mikko Salo) uniqueness result for the fixed angle scattering problem that the acoustic property (zeroth order coefficient) of a medium is uniquely determined by the far-field data, measured in all directions for all frequencies, associated with two incoming plane waves from opposite directions. Next we discuss our (with Venky Krishnan and Soumen Senapati) uniqueness result for a similar problem where the coefficient depends on space and time variables.

Both problems are formally determined and the results are proved by showing Lipschitz stability for two inverse problems for hyperbolic PDEs with boundary data, using a variation of the Bukhgeim-Klibanov method.

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine