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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 4, Pages 116–127 (Mi timm1120)  
This article is cited in 5 scientific papers (total in 5 papers)

Solution asymptotics in a problem of optimal boundary control of a flow through a part of the boundary

A. R. Danilinab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University
Full-text PDF (188 kB) Citations (5)
References:
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Abstract: We consider a problem of optimal control through a part of the boundary of solutions to an elliptic equation in a bounded domain with smooth boundary with a small parameter at the Laplace operator and integral constraints on the control. A complete asymptotic expansion of the solution to this problems in powers of the small parameter is constructed.
Keywords: singular problems, optimal control, boundary value problems for systems of partial differential equations, asymptotic expansions.
Received: 16.05.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 292, Issue 1, Pages 55–66
DOI: https://doi.org/10.1134/S008154381602005X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. R. Danilin, “Solution asymptotics in a problem of optimal boundary control of a flow through a part of the boundary”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 4, 2014, 116–127; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 55–66
Citation in format AMSBIB
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\pages 116--127
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Linking options:
  • https://www.mathnet.ru/eng/timm1120
  • https://www.mathnet.ru/eng/timm/v20/i4/p116
    • This publication is cited in the following 5 articles:
    1. A. R. Danilin, “Asymptotics for solutions of problem on optimally distributed control in convex domain with small parameter at one of higher derivatives”, Ufa Math. J., 15:2 (2023), 42–54  mathnet  crossref
    2. A. R. Danilin, “Asymptotic expansion for the solution of an optimal boundary control problem in a doubly connected domain with different control intensity on boundary segments”, Comput. Math. Math. Phys., 62:2 (2022), 218–231  mathnet  mathnet  crossref  crossref  isi  scopus
    3. Hu W., Shen J., Singler J.R., Zhang Ya., Zheng X., “a Superconvergent Hybridizable Discontinuous Galerkin Method For Dirichlet Boundary Control of Elliptic Pdes”, Numer. Math., 144:2 (2020), 375–411  crossref  mathscinet  zmath  isi  scopus
    4. A. R. Danilin, “Asymptotics of the Solution of a Singular Optimal Distributed Control Problem with Essential Constraints in a Convex Domain”, Diff Equat, 56:2 (2020), 251  crossref
    5. A. R. Danilin, “Asymptotics of the solution of a bisingular optimal boundary control problem in a bounded domain”, Comput. Math. Math. Phys., 58:11 (2018), 1737–1747  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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