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

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2017年第10期25卷 1423-1447页

作者： Hamdi, Adel Inst Natl Sci Appl Rouen Lab Math LMI Ave Univ St Etienne Du Rouvray France

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.

关键词： Non-linear inverse source problem data assimilation optimization and control technique advection-dispersion-reaction equation surface water pollution

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