Null controllability of nonlinear convective heat equations

Sebastian Aniţa; Viorel Barbu

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 157-173
  • ISSN: 1292-8119

Abstract

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The internal and boundary exact null controllability of nonlinear convective heat equations with homogeneous Dirichlet boundary conditions are studied. The methods we use combine Kakutani fixed point theorem, Carleman estimates for the backward adjoint linearized system, interpolation inequalities and some estimates in the theory of parabolic boundary value problems in Lk.

How to cite

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Aniţa, Sebastian, and Barbu, Viorel. "Null controllability of nonlinear convective heat equations." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 157-173. <http://eudml.org/doc/116560>.

@article{Aniţa2010,
abstract = { The internal and boundary exact null controllability of nonlinear convective heat equations with homogeneous Dirichlet boundary conditions are studied. The methods we use combine Kakutani fixed point theorem, Carleman estimates for the backward adjoint linearized system, interpolation inequalities and some estimates in the theory of parabolic boundary value problems in Lk. },
author = {Aniţa, Sebastian, Barbu, Viorel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Null controllability; Carleman estimates; interpolation inequality; Kakutani fixed point theorem.; interpolation inequality; Kakutani fixed point theorem; nonlinear partial differential equation; exact null controllability},
language = {eng},
month = {3},
pages = {157-173},
publisher = {EDP Sciences},
title = {Null controllability of nonlinear convective heat equations},
url = {http://eudml.org/doc/116560},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Aniţa, Sebastian
AU - Barbu, Viorel
TI - Null controllability of nonlinear convective heat equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 157
EP - 173
AB - The internal and boundary exact null controllability of nonlinear convective heat equations with homogeneous Dirichlet boundary conditions are studied. The methods we use combine Kakutani fixed point theorem, Carleman estimates for the backward adjoint linearized system, interpolation inequalities and some estimates in the theory of parabolic boundary value problems in Lk.
LA - eng
KW - Null controllability; Carleman estimates; interpolation inequality; Kakutani fixed point theorem.; interpolation inequality; Kakutani fixed point theorem; nonlinear partial differential equation; exact null controllability
UR - http://eudml.org/doc/116560
ER -

References

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  12. O.Yu. Imanuvilov and M. Yamamoto, On Carleman inequalities for parabolic equations in Sobolev spaces of negative order and exact controllability for semilinear parabolic equations, preprint #98 - 46. University of Tokyo, Grade School of Mathematics, Komobo, Tokyo, Japan (1998).  Zbl1065.35079
  13. O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uraltzeva, Linear and Quasilinear Equations of Paraboic Type. Nauka, Moskow (1967).  
  14. G. Lebeau and L. Robbiano, Contrôle exact de l'équation de la chaleur. Comm. Partial Differential Equations30 (1995) 335-357.  Zbl0819.35071
  15. J.L. Lions, Contrôle des systèmes distribués singuliers, MMI 13. Gauthier-Villars (1983).  
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  17. E. Zuazua, Approximate controllability of the semilinear heat equation: boundary control, in Computational Sciences for the 21st Century, M.O. Bristeau et al., Eds. John Wiley & Sons (1997) 738-747.  Zbl0916.93016
  18. E. Zuazua, Approximate controllability for semilinear heat equations with globally Lipschitz nonlinearities. Control Cybernet., to appear.  Zbl0959.93025

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