@article{AIHPC_2002__19_5_543_0,
author = {L\'opez, A. and Zuazua, E.},
title = {Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {543--580},
year = {2002},
publisher = {Elsevier},
volume = {19},
number = {5},
mrnumber = {1922469},
zbl = {1009.35009},
language = {en},
url = {https://www.numdam.org/item/AIHPC_2002__19_5_543_0/}
}
TY - JOUR AU - López, A. AU - Zuazua, E. TI - Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density JO - Annales de l'I.H.P. Analyse non linéaire PY - 2002 SP - 543 EP - 580 VL - 19 IS - 5 PB - Elsevier UR - https://www.numdam.org/item/AIHPC_2002__19_5_543_0/ LA - en ID - AIHPC_2002__19_5_543_0 ER -
%0 Journal Article %A López, A. %A Zuazua, E. %T Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density %J Annales de l'I.H.P. Analyse non linéaire %D 2002 %P 543-580 %V 19 %N 5 %I Elsevier %U https://www.numdam.org/item/AIHPC_2002__19_5_543_0/ %G en %F AIHPC_2002__19_5_543_0
López, A.; Zuazua, E. Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) no. 5, pp. 543-580. https://www.numdam.org/item/AIHPC_2002__19_5_543_0/
[1] , , , Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène, Asymp. Anal. 5 (1992) 481-494. | Zbl | MR
[2] , Boundary controllability of the one-dimensional wave equation with periodic oscillating density, Asymp. Anal. 20 (1999) 317-350. | Zbl | MR
[3] , , Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace, C. R. Acad. Sci. Paris 324 (1997) 1237-1242. | Zbl | MR
[4] , , Low frequency asymptotic analysis of a string with rapidly oscillating density, SIAM J. Appl. Math. 60 (2000) 1205-1233. | Zbl | MR
[5] , , An Introduction to Homogenization, Oxford Lecture Series in Mathematics and its Applications, 17, 1999. | Zbl | MR
[6] , , , Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh 125 A (1995) 31-61. | Zbl | MR
[7] , Boundary control systems, SIAM J. Contr. 6 (1968) 349-385. | Zbl | MR
[8] , , Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Rational Mech. Anal. 43 (1971) 272-292. | Zbl | MR
[9] , , Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations, Quart. Appl. Mat. 32 (1974) 45-69. | Zbl | MR
[10] , Null controllability of the heat equation, ESAIM: COCV 2 (1997) 87-103. | Zbl | MR | Numdam
[11] , , Controllability of Evolution Equations, Lecture Notes Series, 34, Seoul National University, 1996. | Zbl | MR
[12] , On Moment Theory and Controllability of One-Dimensional Vibrating System and Heating Processes, Lecture Notes in Control and Information Sciences, 173, Springer-Verlag, 1992. | Zbl | MR
[13] , The wave equation with oscillating density: observability at low frequency, ESAIM: COCV 5 (2000) 219-258. | Zbl | MR | Numdam
[14] , , Contrôle exact de l'équation de la chaleur, Comm. PDE 20 (1995) 335-356. | Zbl | MR
[15] , , Null controllability of a system of linear thermoelasticity, Archives Rat. Mech. Anal. 141 (4) (1998) 297-329. | Zbl | MR
[16] , Control y perturbaciones singulares de sistemas parabólicos, Ph.D. Thesis, Universidad Complutense Madrid, 1999.
[17] , , Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating coefficients, C. R. Acad. Sci. Paris, Série I 326 (1998) 955-960. | Zbl | MR
[18] , , , Null controllability of the heat equation as singular limit of the exact controllability of dissipative wave equations, J. Math. Pures Appl. 79 (8) (2000) 741-808. | Zbl | MR
[19] , A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Studies Appl. Math. 52 (1973) 189-221. | Zbl | MR
[20] , Etude des sommes d'exponentielles, Hermann, Paris, 1959. | Zbl | MR






