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 (2010)

  • 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|log3/2(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 (2010): 621-661. <http://eudml.org/doc/90663>.

@article{Doubova2010,
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|log3/2(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.; transmission problems},
language = {eng},
month = {3},
pages = {621-661},
publisher = {EDP Sciences},
title = {Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients},
url = {http://eudml.org/doc/90663},
volume = {8},
year = {2010},
}

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
DA - 2010/3//
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|log3/2(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.; transmission problems
UR - http://eudml.org/doc/90663
ER -

References

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