Comptes Rendus
Partial Differential Equations
Carleman estimates and null controllability for boundary-degenerate parabolic operators
[Estimations de Carleman et nulle contrôlabilité pour une classe d'opérateurs paraboliques dégénérés]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 147-152.

Motivés par de nombreux problèmes venant de la physique, la biologie et de l'économie, nous considérons une classe d'équations paraboliques dont l'opérateur associé dégénère au bord du domaine spatial. Nous étudions la nulle contrôlabilité, établissant en particulier une estimation de Carleman pour l'équation dégénérée adjointe.

Motivated by several examples coming from physics, biology, and economics, we consider a class of parabolic operators that degenerate at the boundary of the space domain. We study null controllability by a locally distributed control. For this purpose, a specific Carleman estimate for the solutions of degenerate adjoint problems is proved.

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DOI : 10.1016/j.crma.2008.12.011

Piermarco Cannarsa 1 ; Partick Martinez 2 ; Judith Vancostenoble 2

1 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
2 Institut de mathématiques de Toulouse, U.M.R. C.N.R.S. 5219, Université Paul-Sabatier Toulouse III, 118, route de Narbonne, 31062 Toulouse cedex 4, France
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Piermarco Cannarsa; Partick Martinez; Judith Vancostenoble. Carleman estimates and null controllability for boundary-degenerate parabolic operators. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 147-152. doi : 10.1016/j.crma.2008.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.011/

[1] P. Cannarsa; P. Martinez; J. Vancostenoble Carleman estimates for a class of degenerate parabolic operators, SIAM J. Control Optim., Volume 47 (2008) no. 1, pp. 1-19

[2] P. Cannarsa, P. Martinez, J. Vancostenoble, Carleman estimates and null controllability for boundary-degenerate parabolic operators, in preparation

[3] P. Cannarsa; D. Rocchetti; J. Vancostenoble Generation of analytic semi-groups in L2 for a class of second order degenerate elliptic operators, Control Cybernet., Volume 37 (2008) no. 4

[4] L. Escauriaza; G. Seregin; V. Šverák Backward uniqueness for the heat operator in half-space, St. Petersburg Math. J., Volume 15 (2004) no. 1, pp. 139-148

[5] A.V. Fursikov; O.Yu. Imanuvilov Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Seoul National University, Seoul, Korea, 1996

[6] G. Lebeau; L. Robbiano Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations, Volume 20 (1995), pp. 335-356

[7] S. Micu; E. Zuazua On the lack of null controllability of the heat equation on the half-space, Portugal. Math., Volume 58 (2001), pp. 1-24

[8] B. Opic; A. Kufner Hardy-Type Inequalities, Pitman Research Notes in Math., vol. 219, Longman, 1990

[9] K.-D. Phung Remarques sur l'observabilité pour l'équation de Laplace, Control Opt. Calc. Var., Volume 9 (2003), pp. 621-635

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