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Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2020, Volume 22, Number 2, Pages 188–199
DOI: https://doi.org/10.15507/2079-6900.22.202002.188-199
(Mi svmo768)
 

Applied mathematics and mechanics

About one method for replacing variables for a wavean equation describing vibrations of systems with moving boundaries

V. N. Anisimov, V. L. Litvinov

Samara State Technical University
References:
Abstract: An analytical method for solving the wave equation describing the oscillations of systems with moving boundaries is considered. By replacing variables that set boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional – difference equations that can be solved using forward and reverse methods. The inverse method is described, which allows us to apply sufficiently diverse laws of boundary motion to the laws obtained from the solution of the inverse problem. New partial solutions for a fairly wide range of boundary motion laws are obtained. A direct asymptotic method for approximating the solution of a functional equation is considered. The errors of the approximate method are estimated depending on the speed of the border movement.
Keywords: wave equation, boundary value problems, oscillation of system with moving boundarie, substitution of variables, law of boundary motion, functional equation.
Bibliographic databases:
Document Type: Article
UDC: 517.958:531.12; 534.11
MSC: Primary 35R37; Secondary 35G30, 35Q70
Language: Russian
Citation: V. N. Anisimov, V. L. Litvinov, “About one method for replacing variables for a wavean equation describing vibrations of systems with moving boundaries”, Zhurnal SVMO, 22:2 (2020), 188–199
Citation in format AMSBIB
\Bibitem{AniLit20}
\by V.~N.~Anisimov, V.~L.~Litvinov
\paper About one method for replacing variables for a wavean equation describing vibrations of systems with moving boundaries
\jour Zhurnal SVMO
\yr 2020
\vol 22
\issue 2
\pages 188--199
\mathnet{http://mi.mathnet.ru/svmo768}
\crossref{https://doi.org/10.15507/2079-6900.22.202002.188-199}
\elib{https://elibrary.ru/item.asp?id=43093594}
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    Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva
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