Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-14T22:27:21.259Z Has data issue: false hasContentIssue false
  • English
  • Français

Sentinels with given sensitivity

Published online by Cambridge University Press:  01 February 2008

G. MASSENGO MOPHOU  and
O. NAKOULIMA
G. MASSENGO MOPHOU
Affiliation:
Département de Mathématiques et Informatique, Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI) email: Gisele.Mophou@univ-ag.fr; onakouli@univ-ag.fr
O. NAKOULIMA
Affiliation:
Département de Mathématiques et Informatique, Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe-à-Pitre Guadeloupe (FWI) email: Gisele.Mophou@univ-ag.fr; onakouli@univ-ag.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

This work is devoted to the identification of parameters in a problem of pollution modeled by a semi-linear parabolic equation. We use the notion of sentinels introduced by J. L. Lions, (Lions, J. L. 1992 Sentinelles pour les systèmes distribués à données incomplètes. Masson, Paris.) re-visited in a more general framework. We prove the existence of such sentinels by solving a problem of null controllability with constraint on the control. The key of our results is an observability inequality of Carleman type adapted to the constraint.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 19 , Issue 1 , February 2008 , pp. 21 - 40
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ainseba, B. E., Kernevez, J. P. & Luce, R. (1994) Application des sentinelles à l'identification des pollutions dans une rivière. M2AN Math Model. Numer. Anal. 28 (3), 297–312.Google Scholar
[2]Ainseba, B. E., Kernevez, J. P. & Luce, R. (1994) Identification de paramètres dans des problèmees non linéaires à données incomplètes. M2AN Math. Model. Numer. Anal. 28 (3), 313–328.Google Scholar
[3]Bodart, O. (1997) Sentinels for the identification of an unknown boundary. Math. Models Methods Appl. Sci. 7 (N6), 871–885.Google Scholar
[4]Cazenave, Th. & Haraux, A. (1990) Introduction aux problèmes d'évolution semi-linéaires, Mathématiques et Applications No. 1, Ellipses, Paris.Google Scholar
[5]Fernandez-Cara, E., González-Burgos, M., Guerrero, S. & Puel, J. P. (1996) Null controllability of the heat equation with boundary Fourier conditions: The linear case. ESAIM: COCV, Vol. 12, No. 3, pp. 442–465.Google Scholar
[6]Fursikov, A. & Imanuvilov, O. Yu. (1996) Controllability of evolution equations. Lecture Notes, Research Institute of Mathematics, Seoul National University, Korea.Google Scholar
[7]Imanuvilov, O. Yu. (1995) Controllability of parabolic equations. Sbornik Math. 186 (6), 879–900.Google Scholar
[8]Lebeau, G. & Robbiano, L. (1995) Contrôle exacte de l'équation de la chaleur. Comm. P.D.E. 20, 335–356.Google Scholar
[9]Lions, J. L. (1992) Sentinelles pour les systèmes distribués à données incomplètes. Masson, Paris.Google Scholar
[10]Lions, J. L. (1971) Optimal Control of Systems Governed Partial Differential Equations. Springer, New York.Google Scholar
[11]Mizohata, S. (1958) Unicité du prolongement des solutions pour quelques équations différentielles paraboliques, Memoirs. Sci. Univ. Kyoto 31, 219–239.Google Scholar
[12]Russell, D. L. (1973) A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Stud. Appl. Math. 52 (3), 189–212.CrossRefGoogle Scholar
[13]Saut, J. C. & Schereur, B. (1987) Unique continuation for some evolution equations. J. Diff. Eq. 66 118–139.CrossRefGoogle Scholar
[14]Tataru, D. (1996) Carleman estimates, unique continuation and contollability for anizotropic PDEs, Optimization methods in partial differential equations. Amer. Math. Soc. 209, 267–279.Google Scholar
[15]Zuazua, E. (1997) Finite dimensional null controllability for the semilinear heat equation. J. Math. Pures Appl. 76, 237–264.CrossRefGoogle Scholar