Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients

Anna Doubova; A. Osses; J.-P. Puel

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • Volume: 8, page 621-661
  • ISSN: 1292-8119

Abstract

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The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion coefficient is the smaller and if the nonlinear term f ( y ) grows slower than | y | log 3 / 2 ( 1 + | y | ) at infinity. In the proof we use null controllability results for the associate linear system and global Carleman estimates with explicit bounds or combinations of several of these estimates. In order to treat the terms appearing on the interface, we have to construct specific weight functions depending on geometry.

How to cite

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Doubova, Anna, Osses, A., and Puel, J.-P.. "Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 621-661. <http://eudml.org/doc/245183>.

@article{Doubova2002,
abstract = {The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion coefficient is the smaller and if the nonlinear term $f(y)$ grows slower than $|y| \log ^\{3/2\}(1+ |y|)$ at infinity. In the proof we use null controllability results for the associate linear system and global Carleman estimates with explicit bounds or combinations of several of these estimates. In order to treat the terms appearing on the interface, we have to construct specific weight functions depending on geometry.},
author = {Doubova, Anna, Osses, A., Puel, J.-P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Carleman inequalities; controllability; transmission problems},
language = {eng},
pages = {621-661},
publisher = {EDP-Sciences},
title = {Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients},
url = {http://eudml.org/doc/245183},
volume = {8},
year = {2002},
}

TY - JOUR
AU - Doubova, Anna
AU - Osses, A.
AU - Puel, J.-P.
TI - Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2002
PB - EDP-Sciences
VL - 8
SP - 621
EP - 661
AB - The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion coefficient is the smaller and if the nonlinear term $f(y)$ grows slower than $|y| \log ^{3/2}(1+ |y|)$ at infinity. In the proof we use null controllability results for the associate linear system and global Carleman estimates with explicit bounds or combinations of several of these estimates. In order to treat the terms appearing on the interface, we have to construct specific weight functions depending on geometry.
LA - eng
KW - Carleman inequalities; controllability; transmission problems
UR - http://eudml.org/doc/245183
ER -

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Citations in EuDML Documents

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  1. Jérôme Le Rousseau, Matthieu Léautaud, Luc Robbiano, Controllability of a parabolic system with a diffusive interface
  2. Ousseynou Nakoulima, Optimal control for distributed systems subject to null-controllability. Application to discriminating sentinels
  3. Viorel Barbu, Exact null internal controllability for the heat equation on unbounded convex domains
  4. Jérôme Le Rousseau, Nicolas Lerner, Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
  5. Jérôme Le Rousseau, Gilles Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
  6. Karine Beauchard, Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type
  7. Jérôme Le Rousseau, Gilles Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

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