[De la contrôlabilité des équations paraboliques linéaires avec une localisation arbitraire du contrôle pour des milieux stratifiés]
Nous prouvons un résultat de contrôlabilité à zéro avec une localisation arbitraire de la zone de contrôle en dimension plus grande que deux pour une classe d'opérateurs paraboliques avec des coefficients non réguliers. Les coefficients sont supposés singuliers dans une seule direction.
We prove a null controllability result with an arbitrary control location in dimension greater than or equal to two for a class of linear parabolic operators with non-smooth coefficients. The coefficients are assumed to be smooth in all but one directions.
Accepté le :
Publié le :
@article{CRMATH_2007__344_6_357_0,
author = {Benabdallah, Assia and Dermenjian, Yves and Le Rousseau, J\'er\^ome},
title = {On the controllability of linear parabolic equations with an arbitrary control location for stratified media},
journal = {Comptes Rendus. Math\'ematique},
pages = {357--362},
publisher = {Elsevier},
volume = {344},
number = {6},
year = {2007},
doi = {10.1016/j.crma.2007.01.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.012/}
}
TY - JOUR AU - Benabdallah, Assia AU - Dermenjian, Yves AU - Le Rousseau, Jérôme TI - On the controllability of linear parabolic equations with an arbitrary control location for stratified media JO - Comptes Rendus. Mathématique PY - 2007 SP - 357 EP - 362 VL - 344 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.01.012/ DO - 10.1016/j.crma.2007.01.012 LA - en ID - CRMATH_2007__344_6_357_0 ER -
%0 Journal Article %A Benabdallah, Assia %A Dermenjian, Yves %A Le Rousseau, Jérôme %T On the controllability of linear parabolic equations with an arbitrary control location for stratified media %J Comptes Rendus. Mathématique %D 2007 %P 357-362 %V 344 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.01.012/ %R 10.1016/j.crma.2007.01.012 %G en %F CRMATH_2007__344_6_357_0
Benabdallah, Assia; Dermenjian, Yves; Le Rousseau, Jérôme. On the controllability of linear parabolic equations with an arbitrary control location for stratified media. Comptes Rendus. Mathématique, Tome 344 (2007) no. 6, pp. 357-362. doi : 10.1016/j.crma.2007.01.012. http://www.numdam.org/articles/10.1016/j.crma.2007.01.012/
[1] Lectures on Elliptic Boundary Values Problems, Van Nostrand, 1965
[2] G. Alessandrini, L. Escauriaza, Null-controllability of one-dimensional parabolic equations, preprint
[3] Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications, C. R. Mecanique, Volume 334 (2006), pp. 582-586
[4] A. Benabdallah, Y. Dermenjian, J. Le Rousseau, Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem, J. Math Anal. Appl., in press
[5] Analyse mathématique et calcul numérique pour les sciences et les techniques, vol. 5, Masson, Paris, 1988
[6] Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, ESAIM: Control Optim. Calc. Var., Volume 8 (2002), pp. 621-661
[7] Global Carleman inequalities for parabolic systems and application to controllability, SIAM J. Control Optim., Volume 45 (2006), pp. 1395-1446
[8] Controllability of Evolution Equations, Lecture Notes, vol. 34, Seoul National University, Korea, 1996
[9] Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations, Volume 20 (1995), pp. 335-356
[10] Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients, J. Differential Equations, Volume 233 (2007), pp. 417-447
[11] Contrôlabilité exacte Perturbations et Stabilisation de systèmes distribués, vol. 1, Masson, Paris, 1988
[12] Methods of Modern Mathematical Physics, vol. 1, Academic Press, San Diego, 1980
Cité par Sources :
