Detection and Location of Moving Point Sources in Contaminant Transport Models. Uniqueness and Minimal Observations

Faker Ben Belgacem (1) , Henda El Fekih (2) , Khiari Souad (1, 2)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne
2 LR-LAMSIN-ENIT - Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]

We are interested in an inverse problem of recovering the position of a pollutant or contaminant source in a stream water. Advection, dispersive transport and the reaction of the solute is commonly modeled by a linear or non-linear parabolic equation. In former works, it is established that a point-wise source is fully identifiable from measurements recorded by a couple of sensors placed, one up-stream and the other down-stream of the pollution source. The observability question we try to solve here is related to the redundancy of sensors when additional information is available on the point-wise source. It may occur, in hydrological engineering, that the intensity of the pollutant is known in advance. In this case, we pursue an identifiability result of a moving source location using a single observation. The chief mathematical tools to prove identifiability are the unique continuation theorem together with an appropriate maximum principle for the parabolic equation under investigation.

Mots clés: Reaction-dispersion equation; point-wise sources; maximum principle; unique continuation theorem; identifiability

Domaines: Analyse numérique [math.NA]

Faker Ben Belgacem, Henda El Fekih, Khiari Souad. Detection and Location of Moving Point Sources in Contaminant Transport Models. Uniqueness and Minimal Observations. 2013. ⟨hal-00818370⟩