We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.
@article{COCV_2008__14_2_284_0,
author = {Alessandrini, Giovanni and Escauriaza, Luis},
title = {Null-controllability of one-dimensional parabolic equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {284--293},
publisher = {EDP-Sciences},
volume = {14},
number = {2},
year = {2008},
doi = {10.1051/cocv:2007055},
mrnumber = {2394511},
zbl = {1145.35337},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007055/}
}
TY - JOUR AU - Alessandrini, Giovanni AU - Escauriaza, Luis TI - Null-controllability of one-dimensional parabolic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 SP - 284 EP - 293 VL - 14 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007055/ DO - 10.1051/cocv:2007055 LA - en ID - COCV_2008__14_2_284_0 ER -
%0 Journal Article %A Alessandrini, Giovanni %A Escauriaza, Luis %T Null-controllability of one-dimensional parabolic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2008 %P 284-293 %V 14 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007055/ %R 10.1051/cocv:2007055 %G en %F COCV_2008__14_2_284_0
Alessandrini, Giovanni; Escauriaza, Luis. Null-controllability of one-dimensional parabolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 284-293. doi : 10.1051/cocv:2007055. http://www.numdam.org/articles/10.1051/cocv:2007055/
[1] and , Riemann's mapping theorem for variable metrics. Ann. Math 72 (1960) 265-296. | MR | Zbl
[2] and , Elliptic equations in divergence form, geometric critical oints of solutions and Stekloff eigenfunctions. SIAM J. Math. Anal 25 (1994) 1259-1268. | MR | Zbl
[3] and , Stable determination of a crack in a planar inhomogeneous conductor. SIAM J. Math. Anal 30 (1998) 326-340. | MR | Zbl
[4] and , On a representation theorem for linear elliptic systems with discontinuous coefficients and applications, in Convegno Internazionale sulle Equazioni alle Derivate Parziali, Cremonese, Roma (1955) 111-138. | MR | Zbl
[5] , and , Partial Differential Equations. Interscience, New York (1964). | MR | Zbl
[6] , Les Fonctions Quasi Analytiques. Gauthier-Villars, Paris (1926). | JFM
[7] and , Concentration and lack of observability of waves in highly heterogeneous media. Arch. Rat. Mech. Anal 164 (2002) 39-72. | MR | Zbl
[8] and , On the null controllability of the one-dimensional heat equation with BV coefficients Comput. Appl. Math. 21 (2002) 167-190. | MR | Zbl
[9] and , Controllability of evolution equations Lecture Notes Series 34, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University (1996). | MR | Zbl
[10] and , Elliptic Partial Differential Equations of Second Order, 2nd edn., Springer-Verlag, Berlin-Heildeberg-New York-Tokyo (1983). | MR | Zbl
[11] and , Carleman estimate for a parabolic equation in Sobolev spaces of negative order and its applications, in Control of Nonlinear Distributed Parameter Systems, G. Chen et al. Eds., Marcel-Dekker (2000) 113-137. | MR | Zbl
[12] and , Generalized analyticity and some related properties of solutions of elliptic and parabolic equations Russian Math. Surv. 29 (1974) 195-212. | MR | Zbl
[13] and , Contrôle exact de l'équation de la chaleur Commun. Partial Differ. Equ. 20 (1995) 335-356. | MR | Zbl
[14] and , Null controllability of a system of linear thermoelasticity Arch. Rat. Mech. Anal. 141 (1998) 297-329. | MR | Zbl
[15] , A uniqueness theorem for parabolic equations Comm. Pure Appl. Math 42 (1988) 125-136. | MR | Zbl
[16] and , Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density Ann. I.H.P. - Analyse non linéaire 19 (2002) 543-580. | EuDML | Numdam | MR | Zbl
[17] , Theory of Functions of a Complex Variable Prentice Hall, Englewood Cliffs, NJ (1965). | MR | Zbl
[18] , A unified boundary controllability theory for hyperbolic and parabolic partial differential equations Stud. Appl. Math. 52 (1973) 189-221. | MR | Zbl
[19] , Potential Theory in Modern Function Theory Maruzen, Tokyo (1959). | MR | Zbl
[20] , Generalized Analytic Functions Pergamon, Oxford (1962). | MR | Zbl
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