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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2024, Volume 327, Pages 229–237
DOI: https://doi.org/10.4213/tm4427 (Mi tm4427) 		 
Special Discontinuities in the Solution of a Self-similar Problem on Waves in a Rod

A. G. Kulikovskii

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tm4427
Abstract: We consider a self-similar problem on small-amplitude long nonlinear longitudinal–torsional waves arising in a semi-infinite elastic rod under a change of stresses at its end. A specific feature of this problem is that among possible discontinuities in its solution, in addition to shocks, a special discontinuity may appear with an additional boundary condition that expresses the existence condition for a stationary viscous structure of this discontinuity.
Keywords: elastic rod, torsional waves, special discontinuity, structure of a discontinuity.
Funding agency
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
Received: May 17, 2024
Revised: May 17, 2024
Accepted: December 10, 2024
Published: 12.03.2025
English version:
Proceedings of the Steklov Institute of Mathematics, 2024, Volume 327, Pages 217–225
DOI: https://doi.org/10.1134/S0081543824060142
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. G. Kulikovskii, “Special Discontinuities in the Solution of a Self-similar Problem on Waves in a Rod”, Mathematical Aspects of Mechanics, Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday, Trudy Mat. Inst. Steklova, 327, Steklov Math. Inst., Moscow, 2024, 229–237; Proc. Steklov Inst. Math., 327 (2024), 217–225
Citation in format AMSBIB
\Bibitem{Kul24}
\by A.~G.~Kulikovskii
\paper Special Discontinuities in the Solution of a Self-similar Problem on Waves in a Rod
\inbook Mathematical Aspects of Mechanics
\bookinfo Collected papers. Dedicated to Dmitry Valerevich Treschev on the occasion of his 60th birthday and to Sergey Vladimirovich Bolotin on the occasion of his 70th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2024
\vol 327
\pages 229--237
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4427}
\crossref{https://doi.org/10.4213/tm4427}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2024
\vol 327
\pages 217--225
\crossref{https://doi.org/10.1134/S0081543824060142}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105001523902}
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