Identification of a time-varying point source in a system of two coupled linear diffusion-advection- reaction equations: application to surface water pollution

Adel Hamdi (1)

1 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

This paper deals with the identification of a point source (localization of its position and recovering the history of its time-varying intensity function) that constitutes the right-hand side of the first equation in a system of two coupled 1D linear transport equations. Assuming that the source intensity function vanishes before reaching the final control time, we prove the identifiability of the sought point source from recording the state relative to the second coupled transport equation at two observation points framing the source region. Note that at least one of the two observation points should be strategic. We establish an identification method that uses these records to identify the source position as the root of a continuous and strictly monotonic function. Whereas the source intensity function is recovered using a recursive formula without any need of an iterative process. Some numerical experiments on a variant of the surface water pollution BOD–OD coupled model are presented.

Domains: Mathematics [math]; Mathematics [math]; Analysis of PDEs [math.AP]; Mathematics [math]; Functional Analysis [math.FA]; Mathematics [math]; Optimization and Control [math.OC]

Adel Hamdi. Identification of a time-varying point source in a system of two coupled linear diffusion-advection- reaction equations: application to surface water pollution. Inverse Problems, 2009, 25 (11), pp.115009. ⟨10.1088/0266-5611/25/11/115009⟩. ⟨hal-02426739⟩