# Null-controllability of one-dimensional parabolic equations

Giovanni Alessandrini; Luis Escauriaza

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 2, page 284-293
- ISSN: 1292-8119

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topAlessandrini, Giovanni, and Escauriaza, Luis. "Null-controllability of one-dimensional parabolic equations." ESAIM: Control, Optimisation and Calculus of Variations 14.2 (2008): 284-293. <http://eudml.org/doc/250362>.

@article{Alessandrini2008,

abstract = {
We prove the interior null-controllability of one-dimensional
parabolic equations with time independent measurable coefficients.
},

author = {Alessandrini, Giovanni, Escauriaza, Luis},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Null-controllability; null-controllability; time independent measurable coefficients},

language = {eng},

month = {3},

number = {2},

pages = {284-293},

publisher = {EDP Sciences},

title = {Null-controllability of one-dimensional parabolic equations},

url = {http://eudml.org/doc/250362},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Alessandrini, Giovanni

AU - Escauriaza, Luis

TI - Null-controllability of one-dimensional parabolic equations

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/3//

PB - EDP Sciences

VL - 14

IS - 2

SP - 284

EP - 293

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

LA - eng

KW - Null-controllability; null-controllability; time independent measurable coefficients

UR - http://eudml.org/doc/250362

ER -

## References

top- L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics. Ann. Math72 (1960) 265–296.
- 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.
- G. Alessandrini and L. Rondi, Stable determination of a crack in a planar inhomogeneous conductor. SIAM J. Math. Anal30 (1998) 326–340.
- 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.
- L. Bers, F. John and M. Schechter, Partial Differential Equations. Interscience, New York (1964).
- T. Carleman, Les Fonctions Quasi Analytiques. Gauthier-Villars, Paris (1926).
- C. Castro and E. Zuazua, Concentration and lack of observability of waves in highly heterogeneous media. Arch. Rat. Mech. Anal164 (2002) 39–72.
- 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.
- 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).
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edn., Springer-Verlag, Berlin-Heildeberg-New York-Tokyo (1983).
- 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.
- 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.
- G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur Commun. Partial Differ. Equ.20 (1995) 335–356.
- G. Lebeau and E. Zuazua, Null controllability of a system of linear thermoelasticity Arch. Rat. Mech. Anal.141 (1998) 297–329.
- F.H. Lin, A uniqueness theorem for parabolic equations Comm. Pure Appl. Math42 (1988) 125–136.
- 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.
- A.I. Markushevich, Theory of Functions of a Complex Variable Prentice Hall, Englewood Cliffs, NJ (1965).
- D.L. Russel, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations Stud. Appl. Math.52 (1973) 189–221.
- M. Tsuji, Potential Theory in Modern Function Theory Maruzen, Tokyo (1959).
- I.N. Vekua, Generalized Analytic Functions Pergamon, Oxford (1962).

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