DMS Applied Mathematics Seminar

Speaker: Mozhgan Entekhabi (Florida A&M University)

Title: Inverse Source Problems for Wave Propagation

Abstract: Inverse source scattering problem arises in many areas of science. It has numerous applications to surface vibrations, acoustical and bio-medical industries, and material science. In particular, inverse source problem seeks the radiating source which produces the measured wave field. This research aims to provide a technique for recovering the source function of the classical elasticity system and the Helmholtz equation from boundary data at multiple wave numbers when the source is compactly supported in an arbitrary bounded C 2 − boundary domain, establish uniqueness for the source from the Cauchy data on any open non empty part of the boundary for arbitrary positive K, and increasing stability when  wave number K is getting large. Various studies showed that the uniqueness can be regained by taking multifrequency boundary measurement in a non-empty frequency interval (0, K) noticing the analyticity of wave-field on the frequency. One of important examples is recovery of acoustic sources from boundary measurement of the pressure. This type of inverse source problem is also motivated by the wide applications in antenna synthesis, medical imaging and geophysics.