Abstract
We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes yield uniqueness of the two unknown elements: the source position and the emitted signal. Using graph theory, we discuss the number and location of the observation nodes. A non-iterative identification method that localizes the source node by solving a set of well posed linear systems is developped. Once the source node is localized, the emitted signal is identified using a deconvolution problem or a Fourier expansion. Numerical experiments on a five node graph confirm the feasability of the approach.
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