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

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.

DOI: https://doi.org/10.4213/sm560

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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

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
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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