Null controllability of the semilinear heat equation

E. Fernández-Cara

ESAIM: Control, Optimisation and Calculus of Variations (1997)

  • Volume: 2, page 87-103
  • ISSN: 1292-8119

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Fernández-Cara, E.. "Null controllability of the semilinear heat equation." ESAIM: Control, Optimisation and Calculus of Variations 2 (1997): 87-103. <http://eudml.org/doc/90516>.

@article{Fernández1997,
author = {Fernández-Cara, E.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {controllability; semilinear heat equation; Schauder's fixed-point theorem},
language = {eng},
pages = {87-103},
publisher = {EDP Sciences},
title = {Null controllability of the semilinear heat equation},
url = {http://eudml.org/doc/90516},
volume = {2},
year = {1997},
}

TY - JOUR
AU - Fernández-Cara, E.
TI - Null controllability of the semilinear heat equation
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1997
PB - EDP Sciences
VL - 2
SP - 87
EP - 103
LA - eng
KW - controllability; semilinear heat equation; Schauder's fixed-point theorem
UR - http://eudml.org/doc/90516
ER -

References

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  1. [1] D. Chae, O.Yu. Imanuvilov and S.M. Kim: Exact controllability for semilinear parabolic equations with Neumann boundary conditions, to appear. Zbl0946.93007MR1420354
  2. [2] C. Fabre, J.P. Puel and E. Zuazua: Approximate controllability of the semilinear heat equation, Proc. Royal Soc. Edinbourgh, 125 A, 1995, 31-61. Zbl0818.93032MR1318622
  3. [3] A.V. Fursikov and O.Yu. Imanuvilov: On controllability of certain Systems simulating a fluid flow, in Flow Control, IMA Vol. Math. Appl., 68, Ed. by M.D. Gunzburger, Springer-Verlag, New York, 1995. Zbl0922.93006MR1348646
  4. [4] A.V. Fursikov and O.Yu. Imanuvilov: Local exact controllability for 2-D Navier-Stokes equations, to appear. 
  5. [5] O.Yu. Imanuvilov: Thesis, Moscow 1991(in russian); 
  6. see also: Exact boundary controllability of the parabolic equation, Russian Math. Surveys, 48, No. 3, 1993, 211-212. 
  7. [6] O.Yu. Imanuvilov: Boundary controllability of parabolic equations, Russian Acad. Sci. Sb. Math., 186, No. 6, 1995, 109-132. Zbl0845.35040MR1349016
  8. [7] O.A. Ladyzhenskaja, V.A. Solonnikov and N.N. Ural'ceva: Linear and quasilinear equations of parabolic type, Trans. Math. Monographs,Vol. 23, AMS, Providence, 1968. Zbl0174.15403
  9. [8] G. Lebeau and L. Robbiano: Contrôle exact de l'équation de la chaleur, Comm. P.D.E., 20, 1995, 335-356. Zbl0819.35071MR1312710
  10. [9] G. Lebeau and E. Zuazua: Null controllability of a system of linear thermoelasticity, Arch. Rat. Mech. Anal., to appear. Zbl1064.93501MR1620510
  11. [10] E. Zuazua: Exact boundary controllability for the semilinear wave equation, in Nonlinear differential equations and their applications, H. Brezis and J.L. Lions eds, Research Notes in Math. 10, Pitman, London, 1991, 357-391. Zbl0731.93011MR1131832
  12. [11] E. Zuazua: Exact controllability for semilinear wave equations in one space dimension, Ann. Inst. Henri Poincaré, Vol. 10, No. 1, 1993, 109-129. Zbl0769.93017MR1212631

Citations in EuDML Documents

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  1. Lionel Rosier, Bing-Yu Zhang, Null controllability of the complex Ginzburg-Landau equation
  2. Sebastian Anita, Viorel Barbu, Null controllability of nonlinear convective heat equations
  3. A. López, E. Zuazua, Uniform null-controllability for the one-dimensional heat equation with rapidly oscillating periodic density
  4. Sebastian Aniţa, Viorel Barbu, Null controllability of nonlinear convective heat equations
  5. Lionel Rosier, Control of the surface of a fluid by a wavemaker
  6. Antonio López, Enrique Zuazua, Some new results related to the null controllability of the 1 - d heat equation
  7. Enrique Fernández-Cara, Enrique Zuazua, Null and approximate controllability for weakly blowing up semilinear heat equations
  8. Lionel Rosier, Control of the surface of a fluid by a wavemaker
  9. Ousseynou Nakoulima, Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels
  10. Alexander Y. Khapalov, Global non-negative controllability of the semilinear parabolic equation governed by bilinear control

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