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Tr. Mat. Inst. Steklova, 2018, Volume 300, Pages 109–122 (Mi tm3860)  

Shock waves in anisotropic cylinders

A. G. Kulikovskii, A. P. Chugainova

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968518010089

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 300, 100–113

Bibliographic databases:

UDC: 519.63
Received: October 9, 2017

Citation: A. G. Kulikovskii, A. P. Chugainova, “Shock waves in anisotropic cylinders”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Tr. Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 109–122; Proc. Steklov Inst. Math., 300 (2018), 100–113

Citation in format AMSBIB
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\paper Shock waves in anisotropic cylinders
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 300
\pages 109--122
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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