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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DNU
2009-08-01
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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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institution | Directory Open Access Journal |
issn | 2312-4547 2415-7325 |
language | English |
last_indexed | 2024-12-13T22:05:24Z |
publishDate | 2009-08-01 |
publisher | DNU |
record_format | Article |
series | Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ |
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 |