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

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

How to cite

top

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

top
  1. L. Ahlfors and L. Bers, Riemann's mapping theorem for variable metrics. Ann. Math72 (1960) 265–296.  Zbl0104.29902
  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.  Zbl0809.35070
  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
  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
  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.  Zbl1016.35003
  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.  Zbl1119.93311
  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).  
  10. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edn., Springer-Verlag, Berlin-Heildeberg-New York-Tokyo (1983).  Zbl0562.35001
  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.  Zbl0977.93041
  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.  
  13. G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur Commun. Partial Differ. Equ.20 (1995) 335–356.  Zbl0819.35071
  14. G. Lebeau and E. Zuazua, Null controllability of a system of linear thermoelasticity Arch. Rat. Mech. Anal.141 (1998) 297–329.  Zbl1064.93501
  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.  Zbl1009.35009
  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).  Zbl0087.28401
  20. I.N. Vekua, Generalized Analytic Functions Pergamon, Oxford (1962).  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.