Geodesic
Stabilizability of a~quasi-linear parabolic equation by means of a~boundary control with feedback
Sbornik. Mathematics, Tome 192 (2001) no. 4, pp. 593-639

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The problem of stabilizability from the boundary $\partial\Omega$ for a parabolic equation given in a bounded domain $\Omega\in\mathbb R^n$, consists in choosing a boundary condition (a control) such that the solution of the resulting mixed boundary-value problem tends as $t\to\infty$ to a given steady-state solution at a prescribed rate $\exp(-\sigma_0t)$. Furthermore, it is required that the control be with feedback, that is, that it react to unpredictable fluctuations of the system by suppressing the results of their action on the stabilizable solution. A new mathematical formulation of the concept of feedback is presented and then used in solving the problem of stabilizability of linear as well as quasi-linear parabolic equations by means of a control with feedback defined on part of the boundary. 
@article{SM_2001_192_4_a6,
     author = {A. V. Fursikov},
     title = {Stabilizability of a~quasi-linear parabolic equation by means of a~boundary control with feedback},
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     publisher = {mathdoc},
     volume = {192},
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     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_4_a6/}
}
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A. V. Fursikov. Stabilizability of a~quasi-linear parabolic equation by means of a~boundary control with feedback. Sbornik. Mathematics, Tome 192 (2001) no. 4, pp. 593-639. http://geodesic.mathdoc.fr/item/SM_2001_192_4_a6/