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 Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 4, Pages 192–202 (Mi timm1013)

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

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.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, 287, suppl. 1, 145–155

Bibliographic databases:

UDC: 517.956.37

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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This publication is cited in the following articles:
1. 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
2. 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
3. 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
4. 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
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