no. 21-22
Partial Differential Equations
Uniqueness for an ill-posed parabolic system
[Unicité pour un système parabolique mal-posé]
Présenté par : Olivier Pironneau
Ben Belgacem, Faker1
1 LMAC, EA 2222, université de technologie de Compiègne, BP 20529, 60205 Compiègne cedex, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1161-1165

The purpose is the uniqueness for an ill-posed parabolic system. This result enables us to state the identifiability for the problem of detecting pointwise organic pollution sources in surface waters.

Lʼobjectif est de prouver lʼunicité de solution pour un système parabolique mal-posé. Ce résultat sert à établir lʼidentifiabilité pour le problème de detection de sources ponctuelles de pollution organique dans les eaux de surface.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.006

Ben Belgacem, Faker 1

1 LMAC, EA 2222, université de technologie de Compiègne, BP 20529, 60205 Compiègne cedex, France 
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Ben Belgacem, Faker. Uniqueness for an ill-posed parabolic system. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1161-1165. doi: 10.1016/j.crma.2011.10.006

[1] Andrle, M.; Ben Belgacem, F.; El Badia, A. Identification of moving point-wise sources in an advection–dispersion–reaction equation, Inverse Problems, Volume 27 (2011), p. 025007

[2] Bernardi, C.; Canuto, C.; Maday, Y. Generalized inf-sup condition for Chebyshev spectral approximation of the Stokes problem, SIAM J. Numer. Anal., Volume 25 (1988), pp. 1237-1271

[3] Brezzi, F.; Fortin, M. Mixed and Hybrid Finite Element Methods, Springer-Verlag, 1991

[4] Dautray, R.; Lions, J.-L. Mathematical Analysis and Numerical Methods for Science and Technology, vol. 5, Springer-Verlag, 1992

[5] Pazy, A. Semi-groups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, 1983 (pp. 100–101)

[6] Streeter, H.W.; Phelps, E.B. A study of the pollution and natural purification of the Ohio river, US Public Health Bull., Volume 146 (1925)

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