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Issue ESAIM: Proc.
Volume 17, 2007
CSVAA 2004 - Control Set-Valued Analysis and Applications
Page(s) 67 - 79
DOI http://dx.doi.org/10.1051/proc:071706
Published online 26 April 2007

ESAIM: Proc., April 2007, Vol. 17, pp. 67-79
DOI: 10.1051/proc:071706

A method for detecting pollution in dissipative systems with incomplete data.

Y. Miloudi1, O. Nakoulima2 and A. Omrane1

1  Département de Mathématiques, Université d'Oran Es-Sénia, BP No 1524 El M'Naouer, 31000 Oran (Algérie), e-mail :
2  Département de Mathématiques et Informatique, Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe à Pitre, Guadeloupe (FWI), e-mail :

miloudi@univ-oran.dz
onakouli@univ-ag.fr
aomrane@univ-ag.fr

(Published online: 26 April 2007)

Abstract
Modelling environmental problems leads to mathematical systems with missing data. For instance, weather problems have generally missing initial conditions. The paper is concerned with identifying pollution terms arising in the state equation of some dissipative system with incomplete initial condition. To this aim the so-called sentinel method is used. Here, the problem of determining a sentinel is equivalent to a null-controllability problem for which Carleman inequalities are revisited.


Résumé
La modélisation des problèmes environmentaux conduit à des systèmes mathématiques à données manquantes. C'est le cas par exemple des problèmes de météorologie où l'on ne connaît jamais la donnée initiale. Nous sommes concernés dans cet article, par l'identification des termes de pollution présents dans l'équation d'état d'un système dissipatif à donnée initiale incomplète. Dans ce but, la méthode des sentinelles de Lions est utilisée. Ici, le problème de détermination d'une sentinelle est équivalent à un problème de contrôlabilité à zéro pour lequel on donne des estimations de type Carleman.


Mathematics Subject Classification. 49K40, 39B35, 35K55, 90C30, 93B05, 64M32

Key words: Dissipative problems, ecosystems, incomplete data, parabolic equation, null-controllability, sentinels, observation, pollution, Carleman inequalities, Inverse problems.


© EDP Sciences, ESAIM 2007


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