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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 502, Pages 11–18
DOI: https://doi.org/10.31857/S2686954322010039 (Mi danma230) 		 
This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

On the homogenization of an optimal control problem in a domain perforated by holes of critical size and arbitrary shape

J. I. Diaza, A. V. Podolskiib, T. A. Shaposhnikova

a Instituto de Matematica Interdisciplinar, Universidad Complutense Madrid, Spain
b Lomonosov Moscow State University, Moscow, Russia
Citations (2)
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DOI: https://doi.org/10.31857/S2686954322010039
Abstract: The paper studies the asymptotic behavior of the optimal control for the Poisson type boundary value problem in a domain perforated by holes of an arbitrary shape with Robin-type boundary conditions on the internal boundaries. The cost functional is assumed to be dependent on the gradient of the state and on the usual norm of the control. We consider the so-called “critical” relation between the problem parameters and the period of the structure $\varepsilon\to0$. Two “strange” terms arise in the limit. The paper extends, by first time in the literature, previous papers devoted to the homogenization of the control problem which always assumed the symmetry of the periodic holes.
Keywords: homogenization, optimal control, perforated domain, strange term, arbitrary shape, critical case.
Funding agency Grant number
Ministry of Science and Innovation of Spanish МТМ2014-57113-Р
МТМ2017-85449-Р
The research of J.I. Díaz was partially supported by the project PID2020-112517GB-I00 (DGISPI, Spain).
Presented: V. V. Kozlov
Received: 30.08.2021
Revised: 27.11.2021
Accepted: 02.12.2021
English version:
Doklady Mathematics, 2022, Volume 105, Issue 1, Pages 6–13
DOI: https://doi.org/10.1134/S1064562422010033
Bibliographic databases:
Document Type: Article
UDC: 517.956.223
Language: Russian
Citation: J. I. Diaz, A. V. Podolskii, T. A. Shaposhnikova, “On the homogenization of an optimal control problem in a domain perforated by holes of critical size and arbitrary shape”, Dokl. RAN. Math. Inf. Proc. Upr., 502 (2022), 11–18; Dokl. Math., 105:1 (2022), 6–13
Citation in format AMSBIB
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\by J.~I.~Diaz, A.~V.~Podolskii, T.~A.~Shaposhnikova
\paper On the homogenization of an optimal control problem in a domain perforated by holes of critical size and arbitrary shape
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 502
\pages 11--18
\mathnet{http://mi.mathnet.ru/danma230}
\crossref{https://doi.org/10.31857/S2686954322010039}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4448456}
\elib{https://elibrary.ru/item.asp?id=48050919}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 1
\pages 6--13
\crossref{https://doi.org/10.1134/S1064562422010033}
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