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Mat. Sb., 2001, Volume 192, Number 4, Pages 115–160 (Mi msb560)  

This article is cited in 39 scientific papers (total in 39 papers)

Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback

A. V. Fursikov

M. V. Lomonosov Moscow State University

Abstract: 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.


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English version:
Sbornik: Mathematics, 2001, 192:4, 593–639

Bibliographic databases:

UDC: 517.977.1
MSC: Primary 35K15, 93D15, 93B52, 35K20; Secondary 35K55, 93B05, 35B37, 47A52, 49N35
Received: 31.08.2000

Citation: A. V. Fursikov, “Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback”, Mat. Sb., 192:4 (2001), 115–160; Sb. Math., 192:4 (2001), 593–639

Citation in format AMSBIB
\by A.~V.~Fursikov
\paper Stabilizability of a~quasi-linear parabolic equation by means of a~boundary control with feedback
\jour Mat. Sb.
\yr 2001
\vol 192
\issue 4
\pages 115--160
\jour Sb. Math.
\yr 2001
\vol 192
\issue 4
\pages 593--639

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    3. A. V. Fursikov, “Stabilizatsiya s granitsy reshenii sistemy Nave-Stoksa: razreshimost i obosnovanie chislennogo modelirovaniya”, Dalnevost. matem. zhurn., 4:1 (2003), 86–100  mathnet  elib
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    12. Fursikov A.V., “Analyticity of stable invariant manifolds of 1D-semilinear parabolic equations”, Control Methods in PDE-Dynamical Systems, Contemporary Mathematics Series, 426, 2007, 219–242  crossref  mathscinet  zmath  isi
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    14. Dymkou V., Pothérat A., “Spectral methods based on the least dissipative modes for wall bounded MHD flows”, Theoret. Comput. Fluid Dynamics, 23:6 (2009), 535–555  crossref  zmath  adsnasa  isi  elib  scopus  scopus  scopus
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  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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