On the instantaneous sentinels in pollution problems of incomplete data

• Published in: Inverse problems in science and engineering Vol. 17; no. 4; pp. 451 - 459
• Main Authors: Miloudi, Y., Nakoulima, O., Omrane, A.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 01.01.2009
• Subjects: boundary value problems; distributed systems of incomplete data; instantaneous sentinels; null-controllability
• ISSN: 1741-5977; 1741-5985
• DOI: 10.1080/17415970802015948

In this work, we discuss how to get instantaneous information (at fixed t = T ∈ [0, +∞[) on pollution terms in distributed systems of incomplete data in some ecology and/or meteorology problems, using the sentinel method of Lions [J.-L. Lions, Sentinelles Pour les Systèmes Distribués à Données Incomplètes, Recherches en mathématiques appliquées RMA No. 21, Masson, Paris, 1992] with control and observation having their supports in two different open sets as by Nakoulima [O. Nakoulima, Contrôlabilité à zéro avec contraintes sur le contrôle, C. R. Acad. Sci. Paris, Ser. I 339 (2004), pp. 405-410]. Here, the ecological system is affected by pollution in the boundary of the domain (e.g. a border of a lake). We verify that if the initial data are completely unknown, the sentinel is null. If there is some information on the initial data, the instantaneous sentinel naturally exists if the control set is bigger than the one where the observation may be defined. Finally, we give the characterization of the instantaneous sentinel with some remarks.