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 $f\left(y\right)$ grows slower than $\left|y\right|{log}^{3/2}(1+|y\left|\right)$ 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.

Keywords: Carleman inequalities, controllability, transmission problems

@article{COCV_2002__8__621_0, author = {Doubova, Anna and Osses, A. and Puel, J.-P.}, title = {Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {621--661}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, doi = {10.1051/cocv:2002047}, mrnumber = {1932966}, zbl = {1092.93006}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2002047/} }

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 SP - 621 EP - 661 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2002047/ DO - 10.1051/cocv:2002047 LA - en ID - COCV_2002__8__621_0 ER -

%0 Journal Article %A Doubova, Anna %A Osses, A. %A Puel, J.-P. %T Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 621-661 %V 8 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2002047/ %R 10.1051/cocv:2002047 %G en %F COCV_2002__8__621_0

Doubova, Anna; Osses, A.; Puel, J.-P. Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients. ESAIM: Control, Optimisation and Calculus of Variations, Volume 8 (2002), pp. 621-661. doi : 10.1051/cocv:2002047. http://www.numdam.org/articles/10.1051/cocv:2002047/

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