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. 
@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},
     publisher = {Elsevier},
     volume = {19},
     number = {5},
     year = {2002},
     mrnumber = {1922469},
     zbl = {1009.35009},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2002__19_5_543_0/}
}
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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. http://www.numdam.org/item/AIHPC_2002__19_5_543_0/

[1] Avellaneda M., Bardos C., Rauch J., Contrôlabilité exacte, homogénéisation et localisation d'ondes dans un milieu non-homogène, Asymp. Anal. 5 (1992) 481-494. | MR | Zbl

[2] Castro C., Boundary controllability of the one-dimensional wave equation with periodic oscillating density, Asymp. Anal. 20 (1999) 317-350. | MR | Zbl

[3] Castro C., Zuazua E., Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace, C. R. Acad. Sci. Paris 324 (1997) 1237-1242. | MR | Zbl

[4] Castro C., Zuazua E., Low frequency asymptotic analysis of a string with rapidly oscillating density, SIAM J. Appl. Math. 60 (2000) 1205-1233. | MR | Zbl

[5] Cioranescu D., Donato P., An Introduction to Homogenization, Oxford Lecture Series in Mathematics and its Applications, 17, 1999. | MR | Zbl

[6] Fabre C., Puel J.P., Zuazua E., Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh 125 A (1995) 31-61. | MR | Zbl

[7] Fattorini H.O., Boundary control systems, SIAM J. Contr. 6 (1968) 349-385. | MR | Zbl

[8] Fattorini H.O., Russell D.L., Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Rational Mech. Anal. 43 (1971) 272-292. | MR | Zbl

[9] Fattorini H.O., Russell D.L., 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. | MR | Zbl

[10] Fernández-Cara E., Null controllability of the heat equation, ESAIM: COCV 2 (1997) 87-103. | Numdam | MR | Zbl

[11] Fursikov A., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes Series, 34, Seoul National University, 1996. | MR | Zbl

[12] Krabs W., On Moment Theory and Controllability of One-Dimensional Vibrating System and Heating Processes, Lecture Notes in Control and Information Sciences, 173, Springer-Verlag, 1992. | MR | Zbl

[13] Lebeau G., The wave equation with oscillating density: observability at low frequency, ESAIM: COCV 5 (2000) 219-258. | Numdam | MR | Zbl

[14] Lebeau G., Robbiano L., Contrôle exact de l'équation de la chaleur, Comm. PDE 20 (1995) 335-356. | MR | Zbl

[15] Lebeau G., Zuazua E., Null controllability of a system of linear thermoelasticity, Archives Rat. Mech. Anal. 141 (4) (1998) 297-329. | MR | Zbl

[16] Lopez A., Control y perturbaciones singulares de sistemas parabólicos, Ph.D. Thesis, Universidad Complutense Madrid, 1999.

[17] López A., Zuazua E., Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating coefficients, C. R. Acad. Sci. Paris, Série I 326 (1998) 955-960. | MR | Zbl

[18] López A., Zhang X., Zuazua E., 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. | MR | Zbl

[19] Russell D.L., A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Studies Appl. Math. 52 (1973) 189-221. | MR | Zbl

[20] Schwartz L., Etude des sommes d'exponentielles, Hermann, Paris, 1959. | MR | Zbl