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Identification of multiple moving pollution sources in surface waters or atmospheric media with boundary observations

We consider the inverse problem of identifying multiple moving pollution sources in a linear advection–dispersion–reaction equation. Although we consider the specific application of pollution source identification in surface waters or atmospheric media, this problem has many other important applications in ecological and diffusive systems. We establish an identifiability result using observations on a non-empty subset of the domain boundary and develop an identification method by reformulating the inverse problem into a minimization problem. Finally, we provide numerical results to support the theoretical results.