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Null-controllability of one-dimensional parabolic equations. (English) Zbl 1145.35337
The null-controllability of one-dimensional parabolic equations with time independent measurable coefficients and control acting in an open subset of the domain is proved.

MSC:
35B37 PDE in connection with control problems (MSC2000)
93B05 Controllability
35K10 Second-order parabolic equations
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[1] L. Ahlfors and L. Bers, Riemann’s mapping theorem for variable metrics. Ann. Math72 (1960) 265-296. · Zbl 0104.29902
[2] G. Alessandrini and R. Magnanini, Elliptic equations in divergence form, geometric critical oints of solutions and Stekloff eigenfunctions. SIAM J. Math. Anal25 (1994) 1259-1268. · Zbl 0809.35070
[3] G. Alessandrini and L. Rondi, Stable determination of a crack in a planar inhomogeneous conductor. SIAM J. Math. Anal30 (1998) 326-340. Zbl0939.35195 · Zbl 0939.35195
[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. Zbl0067.32503 · Zbl 0067.32503
[5] L. Bers, F. John and M. Schechter, Partial Differential Equations. Interscience, New York (1964). · Zbl 0126.00207
[6] T. Carleman, Les Fonctions Quasi Analytiques. Gauthier-Villars, Paris (1926). · JFM 52.0255.02
[7] C. Castro and E. Zuazua, Concentration and lack of observability of waves in highly heterogeneous media. Arch. Rat. Mech. Anal164 (2002) 39-72. · Zbl 1016.35003
[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 1119.93311
[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 0862.49004
[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 0562.35001
[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 0977.93041
[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 0305.35014
[13] G. Lebeau and L. Robbiano, Contrôle exact de l’équation de la chaleur Commun. Partial Differ. Equ.20 (1995) 335-356. · Zbl 0819.35071
[14] G. Lebeau and E. Zuazua, Null controllability of a system of linear thermoelasticity Arch. Rat. Mech. Anal.141 (1998) 297-329. Zbl1064.93501 · Zbl 1064.93501
[15] F.H. Lin, A uniqueness theorem for parabolic equations Comm. Pure Appl. Math42 (1988) 125-136.
[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 linéaire19 (2002) 543-580. · Zbl 1009.35009
[17] A.I. Markushevich, Theory of Functions of a Complex Variable Prentice Hall, Englewood Cliffs, NJ (1965). · Zbl 0142.32602
[18] D.L. Russel, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations Stud. Appl. Math.52 (1973) 189-221. · Zbl 0274.35041
[19] M. Tsuji, Potential Theory in Modern Function Theory Maruzen, Tokyo (1959). · Zbl 0087.28401
[20] I.N. Vekua, Generalized Analytic Functions Pergamon, Oxford (1962). Zbl0100.07603 · Zbl 0100.07603
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