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. 
@article{EMJ_2022_13_3_a3,
     author = {B. E. Kanguzhin},
     title = {Propagation of nonsmooth waves under singular perturbations of the wave equation},
     journal = {Eurasian mathematical journal},
     pages = {41--50},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2022_13_3_a3/}
}
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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/