On stability of one class of optimal control problems to the domain perturbations

On stability of one class of optimal control problems to the domain perturbations

In this paper we study a classical Dirichlet optimal control problem for a nonlinear elliptic equation with the coefficients which we adopt as controls in <em>L</em><em>°°(</em>Ω<em>). </em>The prob­lems of this type have no solutions in general, so we make a spec...

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Bibliographic Details
Main Author: O. P. Kogut
Format: Article
Language:English
Published: DNU 2009-09-01
Series:Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
Subjects:
збурення області
Моско-збіжність просторів Соболева
керування в коефіцієнтах
задача Діріхле
умови стійкості
Online Access:http://model-dnu.dp.ua/index.php/SM/article/view/82
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spelling doaj-b2b61cee89634713a916fe6e66eb92022020-11-24T22:31:30ZengDNUVìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ2312-45472415-73252009-09-01178234110.15421/14090382On stability of one class of optimal control problems to the domain perturbationsO. P. Kogut0Институт прикладного системного анализа НАН Украины и МОН УкраиныIn this paper we study a classical Dirichlet optimal control problem for a nonlinear elliptic equation with the coefficients which we adopt as controls in <em>L</em><em>°°(</em>Ω<em>). </em>The prob­lems of this type have no solutions in general, so we make a special assumption on the coefficients of the state equation and introduce the class of so-called solenoidal controls. We study the stability of the above optimal control problem with respect to the domain perturbation. With this aim we introduce the concept of the Mosco-stability for such problems and study the variational properties of Mosco-stable problems with respect to different types of domain perturbations.http://model-dnu.dp.ua/index.php/SM/article/view/82збурення областіМоско-збіжність просторів Соболевакерування в коефіцієнтахзадача Діріхлеумови стійкості
collection DOAJ
language English
format Article
sources DOAJ
author O. P. Kogut
spellingShingle O. P. Kogut
On stability of one class of optimal control problems to the domain perturbations
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
збурення області
Моско-збіжність просторів Соболева
керування в коефіцієнтах
задача Діріхле
умови стійкості
author_facet O. P. Kogut
author_sort O. P. Kogut
title On stability of one class of optimal control problems to the domain perturbations
title_short On stability of one class of optimal control problems to the domain perturbations
title_full On stability of one class of optimal control problems to the domain perturbations
title_fullStr On stability of one class of optimal control problems to the domain perturbations
title_full_unstemmed On stability of one class of optimal control problems to the domain perturbations
title_sort on stability of one class of optimal control problems to the domain perturbations
publisher DNU
series Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
issn 2312-4547
2415-7325
publishDate 2009-09-01
description In this paper we study a classical Dirichlet optimal control problem for a nonlinear elliptic equation with the coefficients which we adopt as controls in <em>L</em><em>°°(</em>Ω<em>). </em>The prob­lems of this type have no solutions in general, so we make a special assumption on the coefficients of the state equation and introduce the class of so-called solenoidal controls. We study the stability of the above optimal control problem with respect to the domain perturbation. With this aim we introduce the concept of the Mosco-stability for such problems and study the variational properties of Mosco-stable problems with respect to different types of domain perturbations.
topic збурення області
Моско-збіжність просторів Соболева
керування в коефіцієнтах
задача Діріхле
умови стійкості
url http://model-dnu.dp.ua/index.php/SM/article/view/82
work_keys_str_mv AT opkogut onstabilityofoneclassofoptimalcontrolproblemstothedomainperturbations
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