# 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

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topDoubova, 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 -

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