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Mat. Sb., 2003, Volume 194, Number 10, Pages 49–76 (Mi msb773)  

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

Full text: PDF file (419 kB)
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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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\pages 49--76
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\pages 1475--1502
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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