Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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 Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, Number 4, Pages 23–30 (Mi vmumm4412)

Mechanics

Bulgakov problem for a hyperbolic equation and robust stability

V. N. Zhermolenkoa, R. Temoltzi-Avilab

a Gubkin Russian State University of Oil and Gas

Abstract: An inhomogeneous wave equation with dissipation in the presence of an external uncertain perturbation is considered. The problem of finding solutions with the maximum possible amplitudes is investigated. A method for solving this problem based on the Fourier method of separating variables and the Bulgakov problem of the maximum deviation of solutions of second-order ordinary differential equations with external uncertain perturbations is proposed. The application of the Fourier method is justified. The robust stability property of the considered wave equation is investigated.

Key words: external perturbations, Fourier series, maximum deviations.

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UDC: 531.396

Citation: V. N. Zhermolenko, R. Temoltzi-Avila, “Bulgakov problem for a hyperbolic equation and robust stability”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 4, 23–30

Citation in format AMSBIB
\Bibitem{ZheTem21} \by V.~N.~Zhermolenko, R.~Temoltzi-Avila \paper Bulgakov problem for a hyperbolic equation and robust stability \jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh. \yr 2021 \issue 4 \pages 23--30 \mathnet{http://mi.mathnet.ru/vmumm4412}