On the existence of weak optimal BV-controls in coefficients for linear elliptic problems

In this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in <em>BV(Ω). </em>Since the equations of this type can exhibit the Lavren...

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Main Authors: I. G. Balanenko, P. I. Kogut
Format: Article
Language:English
Published: DNU 2009-08-01
Series:Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
Subjects:
Online Access:http://model-dnu.dp.ua/index.php/SM/article/view/87
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author I. G. Balanenko
P. I. Kogut
author_facet I. G. Balanenko
P. I. Kogut
author_sort I. G. Balanenko
collection DOAJ
description In this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in <em>BV(Ω). </em>Since the equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we show that this optimal control problem is regular. Using the direct method in the Calculus of variations, we discuss the solvability of the above optimal control problems in the class of weak admissible solutions.
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spelling doaj.art-6243461a13e242e6998b231e4c03a2f22022-12-21T23:29:51ZengDNUVìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ2312-45472415-73252009-08-011789310310.15421/14090887On the existence of weak optimal BV-controls in coefficients for linear elliptic problemsI. G. Balanenko0P. I. Kogut1Днепропетровский национальный университет имени Олеся ГончараДнепропетровский национальный университет имени Олеся ГончараIn this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in <em>BV(Ω). </em>Since the equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we show that this optimal control problem is regular. Using the direct method in the Calculus of variations, we discuss the solvability of the above optimal control problems in the class of weak admissible solutions.http://model-dnu.dp.ua/index.php/SM/article/view/87optimal control problemdegenerate elliptic equationmixed boundary conditionsLavrentieff phenomenonweak admissible solutions
spellingShingle I. G. Balanenko
P. I. Kogut
On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ
optimal control problem
degenerate elliptic equation
mixed boundary conditions
Lavrentieff phenomenon
weak admissible solutions
title On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_full On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_fullStr On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_full_unstemmed On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_short On the existence of weak optimal BV-controls in coefficients for linear elliptic problems
title_sort on the existence of weak optimal bv controls in coefficients for linear elliptic problems
topic optimal control problem
degenerate elliptic equation
mixed boundary conditions
Lavrentieff phenomenon
weak admissible solutions
url http://model-dnu.dp.ua/index.php/SM/article/view/87
work_keys_str_mv AT igbalanenko ontheexistenceofweakoptimalbvcontrolsincoefficientsforlinearellipticproblems
AT pikogut ontheexistenceofweakoptimalbvcontrolsincoefficientsforlinearellipticproblems