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JOURNALS // Eurasian Mathematical Journal // Archive

Eurasian Math. J., 2022 Volume 13, Number 3, Pages 41–50 (Mi emj445)

This article is cited 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

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.

MSC: 58J32, 35J05, 35J56, 35J08

Received: 26.01.2021

Language: English

DOI: 10.32523/2077-9879-2022-13-3-41-50



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© Steklov Math. Inst. of RAS, 2025