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−σt 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/tk is demonstrated.
Citation:
A. V. Gorshkov, “Stabilization of a semilinear parabolic equation in the exterior of
a bounded domain by means of boundary controls”, Sb. Math., 194:10 (2003), 1475–1502
\Bibitem{Gor03}
\by A.~V.~Gorshkov
\paper Stabilization of a~semilinear parabolic equation in the~exterior of
a~bounded domain by means of boundary controls
\jour Sb. Math.
\yr 2003
\vol 194
\issue 10
\pages 1475--1502
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Linking options:
https://www.mathnet.ru/eng/sm773
https://doi.org/10.1070/SM2003v194n10ABEH000773
https://www.mathnet.ru/eng/sm/v194/i10/p49
This publication is cited in the following 2 articles:
O. V. Gun'ko, V. V. Sulima, “General compactly supported solution of an integral equation of the convolution type”, Diff Equat, 52:9 (2016), 1133
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
Citation in format AMSBIB
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