Geodesic
Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2020), pp. 30-37

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Sufficient matching conditions the time-dependent characteristic first derivatives in the boundary mode with the initial conditions and the more general vibration equation of a semi-bounded string are derived in the sets of solutions of all higher order smoothness orders. They generalize the previously found sufficient matching conditions in the case of a similar mixed problem for the simplest string vibration equation. The characteristic of non-stationary first oblique derivatives in the boundary mode means that at each moment of time they are directed along the critical characteristic.
Keywords: mixed problem; characteristic first oblique derivative; initial conditions; smoothness requirements; matching conditions. 
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     title = {Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
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     publisher = {mathdoc},
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E. V. Ustilko; F. E. Lomovtsev. Matching conditions for values of characteristic oblique derivative at the end of a string, initial data and right-hand side of the wave equation. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2020), pp. 30-37. http://geodesic.mathdoc.fr/item/BGUMI_2020_1_a3/