Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density
López, A. ; Zuazua, E.
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002), p. 543-580 / Harvested from Numdam
@article{AIHPC_2002__19_5_543_0,
     author = {L\'opez, A. and Zuazua, Enrique},
     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},
     volume = {19},
     year = {2002},
     pages = {543-580},
     mrnumber = {1922469},
     zbl = {1009.35009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 543-580. http://gdmltest.u-ga.fr/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 1169354 | Zbl 0763.93006

[2] Castro C., Boundary controllability of the one-dimensional wave equation with periodic oscillating density, Asymp. Anal. 20 (1999) 317-350. | MR 1715339 | Zbl 0940.93016

[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 1456294 | Zbl 1007.93036

[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 1760033 | Zbl 0967.34074

[5] Cioranescu D., Donato P., An Introduction to Homogenization, Oxford Lecture Series in Mathematics and its Applications, 17, 1999. | MR 1765047 | Zbl 0939.35001

[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 1318622 | Zbl 0818.93032

[7] Fattorini H.O., Boundary control systems, SIAM J. Contr. 6 (1968) 349-385. | MR 239249 | Zbl 0164.10902

[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 335014 | Zbl 0231.93003

[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 510972 | Zbl 0281.35009

[10] Fernández-Cara E., Null controllability of the heat equation, ESAIM: COCV 2 (1997) 87-103. | Numdam | MR 1445385 | Zbl 0897.93011

[11] Fursikov A., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes Series, 34, Seoul National University, 1996. | MR 1406566 | Zbl 0862.49004

[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 1162111 | Zbl 0955.93501

[13] Lebeau G., The wave equation with oscillating density: observability at low frequency, ESAIM: COCV 5 (2000) 219-258. | Numdam | MR 1750616 | Zbl 0953.35083

[14] Lebeau G., Robbiano L., Contrôle exact de l'équation de la chaleur, Comm. PDE 20 (1995) 335-356. | MR 1312710 | Zbl 0819.35071

[15] Lebeau G., Zuazua E., Null controllability of a system of linear thermoelasticity, Archives Rat. Mech. Anal. 141 (4) (1998) 297-329. | MR 1620510 | Zbl 1064.93501

[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 1649941 | Zbl 0915.93006

[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 1782102 | Zbl 1079.35017

[19] Russell D.L., A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Studies Appl. Math. 52 (1973) 189-221. | MR 341256 | Zbl 0274.35041

[20] Schwartz L., Etude des sommes d'exponentielles, Hermann, Paris, 1959. | MR 106383 | Zbl 0092.06302