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
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.
wave equation, control problems, observation problems, threshold time, observability inequality, approximate solutions.
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Computational Mathematics and Mathematical Physics, 2014, 54:6, 939–952
MSC: 93C20 (65M06 93B05 93B07 93B40)
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
\by A.~A.~Dryazhenkov, M.~M.~Potapov
\paper Constructive observability inequalities for weak generalized solutions of the wave equation with elastic restraint
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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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
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
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
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