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Comptes Rendus Géoscience
Volume 340, n° 4
pages 245-250 (avril 2008)
Doi : 10.1016/j.crte.2007.11.006
Received : 21 June 2007 ;  accepted : 26 November 2007
Identification of aquifer point sources and partial boundary condition from partial overspecified boundary data
Identification des points sources et d’une condition aux limites sur une partie de la frontière d’un aquifère à partir de conditions aux limites partielles surabondantes

Najla Tlatli Hariga a, Rachida Bouhlila b, , Amel Ben Abda c
a LAMSIN-ENIT & INAT, B.P. 37, 1002 Tunis-Belvedere, Tunisia 
b LMHE-ENIT, B.P. 37, 1002 Tunis-Belvédère, Tunisia 
c LAMSIN-ENIT, B.P. 37, 1002 Tunis-Belvedere, Tunisia 

Corresponding author.

In this work, we present a new mathematical method that allows recovering of the wells fluxes and hydraulic heads on a part of the boundary where they are not known, for an aquifer domain having overspecified boundary data on another part of its boundary. The method is based on the minimisation of an energy-like error functional of Andrieux and Ben Abda [Inverse Probl. 22 (2006) 115–133] for the missing-data recovering step and on the Reciprocity Gap principle of the same authors [Inverse Probl. 12 (1996) 553–564] for point sources identification.

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Nous nous proposons dans ce travail de résoudre un problème de Cauchy, afin de retrouver les débits des puits et la condition de charges imposées sur une partie de la frontière d’un aquifère, à partir de données partielles surabondantes sur une autre partie de la frontière. La résolution se fait en deux étapes : on commence par minimiser la fonctionnelle d’erreur d’énergie développée par Andrieux et Ben Abda [Inverse Probl. 22 (2006) 115–133] pour compléter les données, puis on applique le principe de réciprocité introduit par les mêmes auteurs [Inverse Probl. 12 (1996) 553–564] pour déterminer les débits.

The full text of this article is available in PDF format.

Keywords : Hydrogeology, Inverse problem, Cauchy problem, Data completion, Point sources, Reciprocity gap principle

Mots clés : Hydrogéologie, Problème inverse, Problème de Cauchy, Complétion de données, Points sources, Principe d’écart à la réciprocité

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