Geodesic
Small-amplitude discontinuities of solutions to equations of continuum mechanics
Informatics and Automation, Modern problems and methods in mechanics, Tome 300 (2018), pp. 65-75.

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A general approach is developed for problems of propagation of weak discontinuities against a known background for systems of hyperbolic equations that can be represented in a variational form. A weak shock wave is considered as an approximation to a solution containing a weak discontinuity. This method is applicable to the description of various adiabatic processes in continuum mechanics in the presence of variable force fields. 
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A. N. Golubyatnikov. Small-amplitude discontinuities of solutions to equations of continuum mechanics. Informatics and Automation, Modern problems and methods in mechanics, Tome 300 (2018), pp. 65-75. http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a3/

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