Full paper in PDF format:
$%G. Massengo Mophou and J.-P. Puel, Boundary sentinels with given sensitivity, Rev. Mat. Complut. 22 (2009), no. 1, 165–185.%$

Boundary Sentinels with Given Sensitivity
Gisèle MASSENGO MOPHOU and Jean-Pierre PUEL
Département de Mathématiques et Informatique
Université des Antilles et de La Guyane
Campus Fouillole
97159 Pointe-à-Pitre — Guadeloupe (FWI)

Laboratoire de Mathématiques de Versailles
Université de Versailles St Quentin
45 avenue des Etats Unis
78035 Versailles — France


Received: April 14, 2008
Accepted: July 30, 2008


The notion of sentinels with given sensitivity was introduced by J.-L. Lions in "Sentinelles pour les systèmes distribués à données incomplètes" (1992) in order to identify parameters in a problem of pollution ruled by a semilinear parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. Reconsidering this notion of sentinels in a more general framework, we prove the existence of the new sentinels by solving a boundary null-controllability problem with constraint on the control. Our results use a Carleman inequality which is adapted to the constraint.

Key words: heat equation, optimal control, controllability, Carleman inequalities, sentinels.
2000 Mathematics Subject Classification:
35K05, 35K15, 35K20, 49J20, 93B05.