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Geometry and Topology Seminar: Andrew Shedlock, NC State, Recovery of a complete Riemannian Manifold using the local source-to-solution operator for the Electro-Magnetic Wave Operator
November 10, 2023 | 12:50 pm - 1:10 pm EST
In this talk we consider an Electro-Magnetic Wave operator on a complete Riemannian manifold, which generalizes the standard wave equation to include first order and zeroth order terms. The Cauchy Problem for the Electro-Magnetic Wave operator with zero initial values and a smooth compactly supported forcing function has a unique smooth solution. We study the local source-to-solution operator which maps compactly supported forcing functions on an open observation set to their solutions on this observation set for all time. The local source-to-solution operator allows us to uniquely recover the topology and smooth structure of the complete Riemannian manifold. We are also able to uniquely determine the Riemannian metric and the zeroth order terms. Finally we are able to recover the first order term up to a natural gauge.