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Eurasian Mathematical Journal, 2022, Volume 13, Number 3, Pages 41–50
DOI: https://doi.org/10.32523/2077-9879-2022-13-3-41-50 (Mi emj445) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Propagation of nonsmooth waves under singular perturbations of the wave equation

B. E. Kanguzhin

Al-Farabi Kazakh National University, 71 al-Farabi Ave, 050000 Almaty, Kazakhstan
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DOI: https://doi.org/10.32523/2077-9879-2022-13-3-41-50
Abstract: The method of characteristics for the wave equation can be applied not only for unbounded strings. The method of incident and reflected waves is effectively used in the case of a mixed problem for a bounded string. This method can also be modified for multipoint mixed problems for the wave equation. In this paper, the method of incident and reflected waves is adapted for multi-point problems with discontinuous derivatives. An analogue of the d'Alembert formula for discontinuous multipoint problems for the wave equation in the case of a bounded string is proved.
Keywords and phrases: delta-shaped perturbations, evolution equation, singular perturbations, wave equation.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP08855402
This work was supported by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan, project no. AP08855402.
Received: 26.01.2021
Bibliographic databases:
Document Type: Article
MSC: 58J32, 35J05, 35J56, 35J08
Language: English
Citation: B. E. Kanguzhin, “Propagation of nonsmooth waves under singular perturbations of the wave equation”, Eurasian Math. J., 13:3 (2022), 41–50
Citation in format AMSBIB
\Bibitem{Kan22}
\by B.~E.~Kanguzhin
\paper Propagation of nonsmooth waves under singular perturbations of the wave equation
\jour Eurasian Math. J.
\yr 2022
\vol 13
\issue 3
\pages 41--50
\mathnet{http://mi.mathnet.ru/emj445}
\crossref{https://doi.org/10.32523/2077-9879-2022-13-3-41-50}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4494211}
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