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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 2, Pages 151–158 (Mi timm704)  
This article is cited in 8 scientific papers (total in 8 papers)

Optimal boundary control by displacement at one end of a string under a given elastic force at the other end

E. I. Moiseevab, A. A. Kholomeevab

a Dorodnitsyn Computing Centre of the Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (147 kB) Citations (8)
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Abstract: The problem of optimal boundary control by displacement at one end of a string in the presence of a specified force mode at the other end is studied in the sense of a generalized solution of the corresponding mixed initial- boundary value problem from a Sobolev space. The problem of choosing an optimal boundary control from the infinite number of admissible controls is solved. A generalized solution of the mixed initial-boundary value problem is constructed explicitly and the uniqueness of the solution is proved.
Keywords: optimal control, boundary control, hyperbolic equations, wave equation.
Received: 12.12.2010
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, Volume 276, Issue 1, Pages S153–S160
DOI: https://doi.org/10.1134/S0081543812020125
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: E. I. Moiseev, A. A. Kholomeeva, “Optimal boundary control by displacement at one end of a string under a given elastic force at the other end”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 151–158; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S153–S160
Citation in format AMSBIB
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\paper Optimal boundary control by displacement at one end of a~string under a~given elastic force at the other end
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\issue 2
\pages 151--158
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\jour Proc. Steklov Inst. Math. (Suppl.)
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  • https://www.mathnet.ru/eng/timm704
  • https://www.mathnet.ru/eng/timm/v17/i2/p151
    • This publication is cited in the following 8 articles:
    1. V. I. Korzyuk, J. V. Rudzko, “Classical solution to mixed problems from the theory of longitudinal impact on an elastic semi-infinite rod in the case of separation of the impacting body after the collision”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 60:2 (2024), 95  crossref
    2. M. B. Zvereva, “The Problem of Two-Dimensional String Vibrations with a Nonlinear Condition”, Diff Equat, 59:8 (2023), 1050  crossref
    3. Boyadjiev L., Rashedi K., Sini M., “Estimation of the Time-Dependent Body Force Needed to Exert on a Membrane to Reach a Desired State At the Final Time”, Comput. Methods Appl. Math., 19:2, SI (2019), 323–339  crossref  isi
    4. N. Yessirkegenov, “On a Problem For Wave Equation With Local Data on the Whole Boundary”, Applications of Mathematics in Engineering and Economics, AMEE'16, AIP Conference Proceedings, 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Physics, 2016, UNSP 040006  crossref  mathscinet  isi  scopus
    5. Nurgissa Yessirkegenov, AIP Conference Proceedings, 1759, 2016, 020149  crossref
    6. Yevgenii M. Donchyk, AIP Conference Proceedings, 1690, 2015, 040023  crossref
    7. Moiseev E.I., Kholomeeva A.A., “Solvability of the Mixed Problem for the Wave Equation with a Dynamic Boundary Condition”, Differ. Equ., 48:10 (2012), 1392–1397  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    8. Moiseev E.I., Kholomeeva A.A., “Optimal boundary control by a force at one end of a string with a given force mode at the other end”, Differ. Equ., 47:10 (2011), 1508–1513  crossref  mathscinet  zmath  isi  elib  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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