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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 322, Pages 251–265
DOI: https://doi.org/10.4213/tm4332 (Mi tm4332) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter

A. P. Chugainovaa, R. R. Polekhinaab

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia
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DOI: https://doi.org/10.4213/tm4332
Abstract: We study self-similar solutions of the Riemann problem in the nonuniqueness region for weakly anisotropic elastic media with a negative nonlinearity parameter. We show that all discontinuities contained in the solutions in the nonuniqueness region have a stationary structure. We also show that in the nonuniqueness region one can construct two types of self-similar solutions.
Keywords: shock waves, Riemann problem, nonuniqueness of self-similar solutions.
Funding agency Grant number
Russian Science Foundation 19-71-30012
This work was supported by the Russian Science Foundation under grant no. 19-71-30012, https://rscf.ru/en/project/19-71-30012/, and performed at the Steklov Mathematical Institute of Russian Academy of Sciences.
Received: March 31, 2023
Revised: April 15, 2023
Accepted: May 2, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 322, Pages 242–256
DOI: https://doi.org/10.1134/S008154382304020X
Bibliographic databases:
Document Type: Article
UDC: 531.32
Language: Russian
Citation: A. P. Chugainova, R. R. Polekhina, “Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter”, Modern Methods of Mechanics, Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii, Trudy Mat. Inst. Steklova, 322, Steklov Math. Inst., Moscow, 2023, 251–265; Proc. Steklov Inst. Math., 322 (2023), 242–256
Citation in format AMSBIB
\Bibitem{ChuPol23}
\by A.~P.~Chugainova, R.~R.~Polekhina
\paper Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter
\inbook Modern Methods of Mechanics
\bookinfo Collected papers. On the occasion of the 90th birthday of Academician Andrei Gennad'evich Kulikovskii
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 322
\pages 251--265
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4332}
\crossref{https://doi.org/10.4213/tm4332}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4677609}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 322
\pages 242--256
\crossref{https://doi.org/10.1134/S008154382304020X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85178032719}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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