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Zbl 0817.92017
Ainseba, B.-E.; Kernevez, J.-P.; Luce, R.
Application of sentinels to identification of pollutions in a river. (Application des sentinelles à l'identification des pollutions dans une rivière.) (French. English summary)
[J] RAIRO, Modélisation Math. Anal. Numér. 28, No.3, 297-312 (1994). ISSN 0764-583X

Summary: The aim of this paper is to look at the identification of pollutions in a river. The initial conditions and some boundary conditions are not well determined, thus the model used here is incomplete. The pollution sources can be considered as functionals whose position and nature are known, their amplitudes being however unknown. The goal is to estimate these amplitudes since the other missing terms are of no interest to us. There are two possible approaches to this problem, one is the more classical and uses the least square method, the other, more suited to our problem, is the Sentinel Method introduced by {\it J. L. Lions} [Sentinelles pour les systèmes distribués. (1992; Zbl 0759.93043); C. R. Acad. Sci., Paris, Sér. 307, No. 17, 865-870 (1988; Zbl 0681.93005)]. \par In the first part we apply the Sentinel Method to a model which governs the concentration of the biological oxygen demand in water, denoted here by D.B.O., with a river considered as one-dimensional. The two- dimensional case is looked at the second part. In the third part we take into account not only the D.B.O. but also the oxygen deficit and the nitrate concentration, which is more realistic. In the last part, the solution computed by the least square method is compared with the one obtained with the Sentinel Method.

MSC 2000:: *92D40 Ecology
35R30 Inverse problems for PDE
93C20 Control systems governed by PDE
65K10 Optimization techniques (numerical methods)

Keywords: sentinel method; identification of pollutions; river; least square method; oxygen demand; oxygen deficit; nitrate concentration

Citations: Zbl 0759.93043; Zbl 0681.93005

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