The investigator proposes studying a formally determined inverse problem for the plasma wave equation (wave operator plus a zeroth order term) in three space dimensions. The goal is the recovery of a potential, supported in a ball, from time dependent data generated by coincident source-receiver pairs placed on the boundary of the ball. This problem is an imitation, in the time domain, of the frequency domain problem of recovering a potential from back-scattering data. The investigator will study, the analyticity of the map sending potentials to the data, necessary conditions for a function to be in the range of this map, uniqueness when the potentials are restricted to functions which are analytic in the angular variables, and the recovery of the singularities of the potential from the data.
The solution of the problems proposed by the investigator and the techniques introduced to solve them would be useful in geophysics, oil exploration, medical imaging, defense and other fields where hidden objects are probed by acoustic or electromagnetic waves.
