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

Abstract

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

How to cite

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Alessandrini, 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

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

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