Geodesic
Shock waves in anisotropic cylinders
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 109-122

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We study small-amplitude longitudinal and torsional shock waves in circular cylinders consisting of an anisotropic medium such that the velocities of the longitudinal and torsional waves are close to each other. Previously, simple waves were considered in the same situation and conditions were found for these waves to overturn and for the corresponding shock waves to form. Here we present the study of shock waves: the shock adiabat and the evolutionary conditions. The results obtained can also be related to shock waves in unbounded media with quadratic nonlinearity. 
@article{TM_2018_300_a7,
     author = {A. G. Kulikovskii and A. P. Chugainova},
     title = {Shock waves in anisotropic cylinders},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {109--122},
     publisher = {mathdoc},
     volume = {300},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_300_a7/}
}
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A. G. Kulikovskii; A. P. Chugainova. Shock waves in anisotropic cylinders. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems and methods in mechanics, Tome 300 (2018), pp. 109-122. http://geodesic.mathdoc.fr/item/TM_2018_300_a7/