Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density
Annales de l'I.H.P. Analyse non linéaire (2002)
- Volume: 19, Issue: 5, page 543-580
- ISSN: 0294-1449
Access Full Article
topHow to cite
topReferences
top- [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. Zbl0763.93006MR1169354
- [2] Castro C., Boundary controllability of the one-dimensional wave equation with periodic oscillating density, Asymp. Anal.20 (1999) 317-350. Zbl0940.93016MR1715339
- [3] Castro C., Zuazua E., Contrôle de l'équation des ondes à densité rapidement oscillante à une dimension d'espace, C. R. Acad. Sci. Paris324 (1997) 1237-1242. Zbl1007.93036MR1456294
- [4] Castro C., Zuazua E., Low frequency asymptotic analysis of a string with rapidly oscillating density, SIAM J. Appl. Math.60 (2000) 1205-1233. Zbl0967.34074MR1760033
- [5] Cioranescu D., Donato P., An Introduction to Homogenization, Oxford Lecture Series in Mathematics and its Applications, 17, 1999. Zbl0939.35001MR1765047
- [6] Fabre C., Puel J.P., Zuazua E., Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinburgh125 A (1995) 31-61. Zbl0818.93032MR1318622
- [7] Fattorini H.O., Boundary control systems, SIAM J. Contr.6 (1968) 349-385. Zbl0164.10902MR239249
- [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. Zbl0231.93003MR335014
- [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. Zbl0281.35009MR510972
- [10] Fernández-Cara E., Null controllability of the heat equation, ESAIM: COCV2 (1997) 87-103. Zbl0897.93011MR1445385
- [11] Fursikov A., Imanuvilov O.Yu., Controllability of Evolution Equations, Lecture Notes Series, 34, Seoul National University, 1996. Zbl0862.49004MR1406566
- [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. Zbl0955.93501MR1162111
- [13] Lebeau G., The wave equation with oscillating density: observability at low frequency, ESAIM: COCV5 (2000) 219-258. Zbl0953.35083MR1750616
- [14] Lebeau G., Robbiano L., Contrôle exact de l'équation de la chaleur, Comm. PDE20 (1995) 335-356. Zbl0819.35071MR1312710
- [15] Lebeau G., Zuazua E., Null controllability of a system of linear thermoelasticity, Archives Rat. Mech. Anal.141 (4) (1998) 297-329. Zbl1064.93501MR1620510
- [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 I326 (1998) 955-960. Zbl0915.93006MR1649941
- [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. Zbl1079.35017MR1782102
- [19] Russell D.L., A unified boundary controllability theory for hyperbolic and parabolic partial differential equations, Studies Appl. Math.52 (1973) 189-221. Zbl0274.35041MR341256
- [20] Schwartz L., Etude des sommes d'exponentielles, Hermann, Paris, 1959. Zbl0092.06302MR106383