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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 6, Pages 928–941 (Mi zvmmf10046)  

This article is cited in 3 scientific papers (total in 3 papers)

Constructive observability inequalities for weak generalized solutions of the wave equation with elastic restraint

A. A. Dryazhenkov, M. M. Potapov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: Problems with one-sided boundary controls and a homogeneous Robin boundary condition set on the uncontrolled end are considered in the class of strong generalized solutions of the variable coefficient wave equation. In the adjoint class of weak generalized solutions of the dual problems with one-sided observations, new constructive observability inequalities are obtained that differ from previously known ones by an optimal threshold time. It is shown that, in the considered functional classes, the estimated constants degenerate as the time interval length approaches the threshold. Numerical illustrations are given showing that the stability of approximate solutions to control problems can be substantially enhanced by taking into account a priori information contained in the resulting observability inequalities.

Key words: wave equation, control problems, observation problems, threshold time, observability inequality, approximate solutions.

DOI: https://doi.org/10.7868/S0044466914060064

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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:6, 939–952

Bibliographic databases:

UDC: 519.626
MSC: 93C20 (65M06 93B05 93B07 93B40)
Received: 21.01.2014

Citation: A. A. Dryazhenkov, M. M. Potapov, “Constructive observability inequalities for weak generalized solutions of the wave equation with elastic restraint”, Zh. Vychisl. Mat. Mat. Fiz., 54:6 (2014), 928–941; Comput. Math. Math. Phys., 54:6 (2014), 939–952

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Dryazhenkov, M. M. Potapov, “Numerical solution of the positional boundary control problem for the wave equation with unknown initial data”, Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 22–30  mathnet  crossref  crossref  mathscinet  isi  elib
    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. Andrey A. Dryazhenkov, Mikhail M. Potapov, “A stable method for linear equation in Banach spaces with smooth norms”, Ural Math. J., 4:2 (2018), 56–68  mathnet  crossref  mathscinet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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