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This article is cited in 1 scientific paper (total in 1 paper)
Stabilization of a semilinear parabolic equation in the exterior of
a bounded domain by means of boundary controls
A. V. Gorshkov
M. V. Lomonosov Moscow State University
Abstract:
The problem of the stabilization of a semilinear equation in the exterior of a bounded domain is considered. In view of the impossibility of an exponential stabilization of the form $e^{-\sigma t}$ of the solution of a parabolic equation in an unbounded domain no matter what the boundary control is, one poses the problem of power-like stabilization by means of a boundary control. For a fixed initial condition and parameter $k>0$
of the rate of stabilization the existence of a boundary control
such that the solution approaches zero at the rate $1/t^k$ is demonstrated.
DOI:
https://doi.org/10.4213/sm773
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English version:
Sbornik: Mathematics, 2003, 194:10, 1475–1502
Bibliographic databases:
   
UDC:
517.956.4
MSC: Primary 35K55, 93C20; Secondary 35B40
Received: 25.02.2003
Citation:
A. V. Gorshkov, “Stabilization of a semilinear parabolic equation in the exterior of
a bounded domain by means of boundary controls”, Mat. Sb., 194:10 (2003), 49–76; Sb. Math., 194:10 (2003), 1475–1502
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb773https://doi.org/10.4213/sm773 http://mi.mathnet.ru/eng/msb/v194/i10/p49
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This publication is cited in the following articles:
-
A. V. Gorshkov, “Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary”, Sb. Math., 203:9 (2012), 1244–1268
 
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