17.4 Andrew Shedlock: Title: An Inverse Problem for the Electro-Magnetic Wave Operator using the Local Source-to-Solution Operator

Abstract: We consider the inverse problem of determining the topology, smooth and Riemannian structure of a complete Riemannian manifold and the coefficients of an Electromagnetic Wave Operator using a local source-to-solution operator which maps a source function to its unique solution to an Inhomogeneous Electromagnetic Wave equation on some fixed observation space for all time. The Electromagnetic Wave equation generalizes the classical wave equation by incorporating magnetic field potentials and voltage potentials into the lower terms of the electromagnetic wave equation. We show that the local source-to-solution operator uniquely determines the topological, smooth and Riemannian structure of the manifold up to a Riemannian isometry and show what the natural gauge of the inverse problem is for the lower order terms.