Geodesic
Propagation of nonsmooth waves under singular perturbations of the wave equation
Eurasian mathematical journal, Tome 13 (2022) no. 3, pp. 41-50.

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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. 
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B. E. Kanguzhin. Propagation of nonsmooth waves under singular perturbations of the wave equation. Eurasian mathematical journal, Tome 13 (2022) no. 3, pp. 41-50. http://geodesic.mathdoc.fr/item/EMJ_2022_13_3_a3/

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