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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 4, Pages 192–202 (Mi timm1013)  
This article is cited in 4 scientific papers (total in 4 papers)

Problems of two-sided boundary control for the wave equation on subcritical intervals in classes of strong generalized solutions

M. M. Potapov, D. A. Ivanov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (185 kB) Citations (4)
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Abstract: Problems with two-sided boundary controls of three main types are considered for the wave equation with variables coefficients. Constructive inequalities for the bounded invertibility of the control operator with known (computable) values of estimate constants are obtained in classes of strong generalized solutions on intervals of subcritical length. The obtained estimates make it possible to use the variational method for finding stable numerical solutions to the problems under consideration on time intervals of any subcritical or exactly critical length.
Keywords: wave equation, boundary control, subcritical interval, bounded invertibility inequality, variational method.
Received: 22.01.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 287, Issue 1, Pages 145–155
DOI: https://doi.org/10.1134/S0081543814090144
Bibliographic databases:
Document Type: Article
UDC: 517.956.37
Language: Russian
Citation: M. M. Potapov, D. A. Ivanov, “Problems of two-sided boundary control for the wave equation on subcritical intervals in classes of strong generalized solutions”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 192–202; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 145–155
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/timm/v19/i4/p192
    • This publication is cited in the following 4 articles:
    1. A. A. Dryazhenkov, “Numerical solution to the positional control problem for the wave equation with unknown Robin coefficients”, IFAC-PapersOnLine, 51:32 (2018), 687–691  crossref  isi
    2. D. A. Ivanov, M. M. Potapov, “Approximations to time-optimal boundary controls for weak generalized solutions of the wave equation”, Comput. Math. Math. Phys., 57:4 (2017), 607–625  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. A. Dryazhenkov, M. M. Potapov, “Numerical method for a quadratic minimization problem with an ellipsoidal constraint and an a priori estimate for the solution norm”, Comput. Math. Math. Phys., 56:2 (2016), 206–220  mathnet  crossref  crossref  isi  elib
    4. D. A. Ivanov, M. M. Potapov, “Approximate solution to a time optimal boundary control problem for the wave equation”, Proc. Steklov Inst. Math., 291 (2015), 102–117  mathnet  crossref  crossref  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :102
    References:76
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