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Mat. Sb., 2000, Volume 191, Number 10, Pages 3–12 (Mi msb512)  

This article is cited in 12 scientific papers (total in 12 papers)

Approximation of a singularly perturbed elliptic problem of optimal control

A. R. Danilin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: A problem of optimal control of solutions of an elliptic equation with a small parameter at higher derivatives is considered in a rectangle with two sides parallel to the characteristic of the limit equation. The limit problem is found and asymptotic estimates for solutions of a problem that approximates the original problem are obtained.

DOI: https://doi.org/10.4213/sm512

Full text: PDF file (226 kB)
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English version:
Sbornik: Mathematics, 2000, 191:10, 1421–1431

Bibliographic databases:

UDC: 517.977
MSC: Primary 49K20, 35B37, 93C20; Secondary 35B25, 35C20, 49J20, 93C73
Received: 31.05.1999 and 30.12.1999

Citation: A. R. Danilin, “Approximation of a singularly perturbed elliptic problem of optimal control”, Mat. Sb., 191:10 (2000), 3–12; Sb. Math., 191:10 (2000), 1421–1431

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. R. Danilin, “Asymptotic behaviour of solutions of a singular elliptic system in a rectangle”, Sb. Math., 194:1 (2003), 31–61  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. R. Danilin, “Approximation of a singularly perturbed elliptic optimal control problem with geometric constraints on the control”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S45–S53  mathnet  mathscinet  zmath  elib
    3. M. G. Dmitriev, G. A. Kurina, “Singular perturbations in control problems”, Autom. Remote Control, 67:1 (2006), 1–43  mathnet  crossref  mathscinet  zmath  elib  elib
    4. A. R. Danilin, A. P. Zorin, “Asymptotics of a solution to an optimal boundary control problem”, Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S81–S94  mathnet  crossref  elib
    5. Danilin A.R., Zorin A.P., “Asymptotic Expansion of Solutions to Optimal Boundary Control Problems”, Doklady Mathematics, 84:2 (2011), 665–668  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. A. R. Danilin, A. P. Zorin, “Asimptotika resheniya zadachi optimalnogo granichnogo upravleniya v ogranichennoi oblasti”, Tr. IMM UrO RAN, 18, no. 3, 2012, 75–82  mathnet  elib
    7. A. P. Zorin, “Asimptoticheskoe razlozhenie resheniya zadachi optimalnogo upravleniya ogranichennym potokom na granitse”, Tr. IMM UrO RAN, 19, no. 1, 2013, 115–120  mathnet  mathscinet  elib
    8. A. R. Danilin, N. S. Korobitsyna, “Asymptotic estimates for a solution of a singular perturbation optimal control problem on a closed interval under geometric constraints”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S58–S67  mathnet  crossref  mathscinet  isi  elib
    9. A. R. Danilin, “Asymptotic expansion of a solution to a singular perturbation optimal control problem on an interval with integral constraint”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 66–76  mathnet  crossref  mathscinet  isi  elib
    10. A. R. Danilin, “Solution asymptotics in a problem of optimal boundary control of a flow through a part of the boundary”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 55–66  mathnet  crossref  mathscinet  isi  elib
    11. A. R. Danilin, “Asymptotics of the solution to the singular problem of optimal distributed control in a convex domain”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 72–87  mathnet  crossref  crossref  isi  elib
    12. A. R. Danilin, “Asimptoticheskoe razlozhenie resheniya singulyarno vozmuschennoi zadachi optimalnogo upravleniya s malym koeffitsientom koertsitivnosti”, Tr. IMM UrO RAN, 24, no. 3, 2018, 51–61  mathnet  crossref  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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