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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| Format: | Article |
| Language: | English |
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DNU
2009-09-01
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| Series: | Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ |
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| Online Access: | http://model-dnu.dp.ua/index.php/SM/article/view/82 |
| Summary: | 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. |
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| ISSN: | 2312-4547 2415-7325 |