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Detection-Identification of multiple unknown time-dependent point sources in a 2 D transport equation: application to accidental pollution

Abstract : We address the nonlinear inverse source problem of identifying multiple unknown time-dependent point sources occurring in a two-dimensional evolution advection–dispersion–reaction equation. Provided to be available within the monitored domain interfaces for recording the generated state and its flux crossing each suspected zone where a source could occur, we establish a constructive identifiability theorem based on an introduced dispersion-current function that yields uniqueness of the unknown elements defining all occurring sources. Then, the established theorem leads to develop a detection-identification method that goes throughout the monitored domain to detect in each suspected zone whether there exists or not an occurring source. Once a source is detected, the developed method determines lower and upper bounds of the mean value discharged by its unknown time-dependent intensity function. Thereafter, the method localizes the sought position of the detected source as the unique solution of an equation satisfied by the introduced dispersion-current function and identifies its unknown intensity function from solving an associated deconvolution problem. Ultimately, the unknown number of occurring sources is deduced as the sum of all detected-identified active sources. Some numerical experiments on a variant of the surface water BOD pollution model are presented.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02426059
Contributor : Adel Hamdi <>
Submitted on : Wednesday, January 1, 2020 - 2:29:49 PM
Last modification on : Friday, April 24, 2020 - 1:48:21 AM

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Adel Hamdi. Detection-Identification of multiple unknown time-dependent point sources in a 2 D transport equation: application to accidental pollution. Inverse Problems in Science and Engineering, Taylor & Francis, 2016, 25 (10), pp.1423-1447. ⟨10.1080/17415977.2016.1265957⟩. ⟨hal-02426059⟩

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