[Estimations de Carleman et nulle contrôlabilité pour une classe d'opérateurs paraboliques dégénérés]
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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@article{CRMATH_2009__347_3-4_147_0,
author = {Cannarsa, Piermarco and Martinez, Partick and Vancostenoble, Judith},
title = {Carleman estimates and null controllability for boundary-degenerate parabolic operators},
journal = {Comptes Rendus. Math\'ematique},
pages = {147--152},
publisher = {Elsevier},
volume = {347},
number = {3-4},
year = {2009},
doi = {10.1016/j.crma.2008.12.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.12.011/}
}
TY - JOUR AU - Cannarsa, Piermarco AU - Martinez, Partick AU - Vancostenoble, Judith TI - Carleman estimates and null controllability for boundary-degenerate parabolic operators JO - Comptes Rendus. Mathématique PY - 2009 SP - 147 EP - 152 VL - 347 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.12.011/ DO - 10.1016/j.crma.2008.12.011 LA - en ID - CRMATH_2009__347_3-4_147_0 ER -
%0 Journal Article %A Cannarsa, Piermarco %A Martinez, Partick %A Vancostenoble, Judith %T Carleman estimates and null controllability for boundary-degenerate parabolic operators %J Comptes Rendus. Mathématique %D 2009 %P 147-152 %V 347 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.12.011/ %R 10.1016/j.crma.2008.12.011 %G en %F CRMATH_2009__347_3-4_147_0
Cannarsa, Piermarco; Martinez, Partick; Vancostenoble, Judith. Carleman estimates and null controllability for boundary-degenerate parabolic operators. Comptes Rendus. Mathématique, Tome 347 (2009) no. 3-4, pp. 147-152. doi : 10.1016/j.crma.2008.12.011. http://www.numdam.org/articles/10.1016/j.crma.2008.12.011/
[1] 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] Generation of analytic semi-groups in for a class of second order degenerate elliptic operators, Control Cybernet., Volume 37 (2008) no. 4
[4] Backward uniqueness for the heat operator in half-space, St. Petersburg Math. J., Volume 15 (2004) no. 1, pp. 139-148
[5] Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Seoul National University, Seoul, Korea, 1996
[6] Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations, Volume 20 (1995), pp. 335-356
[7] On the lack of null controllability of the heat equation on the half-space, Portugal. Math., Volume 58 (2001), pp. 1-24
[8] Hardy-Type Inequalities, Pitman Research Notes in Math., vol. 219, Longman, 1990
[9] Remarques sur l'observabilité pour l'équation de Laplace, Control Opt. Calc. Var., Volume 9 (2003), pp. 621-635
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