no. 2
Null-controllability of one-dimensional parabolic equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 2, pp. 284-293

We prove the interior null-controllability of one-dimensional parabolic equations with time independent measurable coefficients.

DOI : 10.1051/cocv:2007055
Classification : 35B37
Keywords: null-controllability 
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     title = {Null-controllability of one-dimensional parabolic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {284--293},
     year = {2008},
     publisher = {EDP Sciences},
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     number = {2},
     doi = {10.1051/cocv:2007055},
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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

[1] L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics. Ann. Math 72 (1960) 265-296. | Zbl | MR

[2] G. Alessandrini and R. Magnanini, Elliptic equations in divergence form, geometric critical oints of solutions and Stekloff eigenfunctions. SIAM J. Math. Anal 25 (1994) 1259-1268. | Zbl | MR

[3] G. Alessandrini and L. Rondi, Stable determination of a crack in a planar inhomogeneous conductor. SIAM J. Math. Anal 30 (1998) 326-340. | Zbl | MR

[4] L. Bers and L. Nirenberg, 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. | Zbl | MR

[5] L. Bers, F. John and M. Schechter, Partial Differential Equations. Interscience, New York (1964). | Zbl | MR

[6] T. Carleman, Les Fonctions Quasi Analytiques. Gauthier-Villars, Paris (1926). | JFM

[7] C. Castro and E. Zuazua, Concentration and lack of observability of waves in highly heterogeneous media. Arch. Rat. Mech. Anal 164 (2002) 39-72. | Zbl | MR

[8] E. Fernandez-Cara and E. Zuazua, On the null controllability of the one-dimensional heat equation with BV coefficients Comput. Appl. Math. 21 (2002) 167-190. | Zbl | MR

[9] A.V. Fursikov and O. Yu. Imanuvilov, Controllability of evolution equations Lecture Notes Series 34, Research Institute of Mathematics, Global Analysis Research Center, Seoul National University (1996). | Zbl | MR

[10] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edn., Springer-Verlag, Berlin-Heildeberg-New York-Tokyo (1983). | Zbl | MR

[11] O.Yu. Imanuvilov and M. Yamamoto, 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. | Zbl | MR

[12] E.M. Landis and O.A. Oleinik, Generalized analyticity and some related properties of solutions of elliptic and parabolic equations Russian Math. Surv. 29 (1974) 195-212. | Zbl | MR

[13] G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur Commun. Partial Differ. Equ. 20 (1995) 335-356. | Zbl | MR

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

[15] F.H. Lin, A uniqueness theorem for parabolic equations Comm. Pure Appl. Math 42 (1988) 125-136. | Zbl | MR

[16] A. López and E. Zuazua, 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. | Numdam | Zbl | MR | EuDML

[17] A.I. Markushevich, Theory of Functions of a Complex Variable Prentice Hall, Englewood Cliffs, NJ (1965). | Zbl | MR

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

[19] M. Tsuji, Potential Theory in Modern Function Theory Maruzen, Tokyo (1959). | Zbl | MR

[20] I.N. Vekua, Generalized Analytic Functions Pergamon, Oxford (1962). | Zbl | MR

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