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Sbornik: Mathematics, 2021, Volume 212, Issue 4, Pages 475–489
DOI: https://doi.org/10.1070/SM9383 (Mi sm9383) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Constructing unbounded discontinuous solutions of scalar conservation laws using the Legendre transform

L. V. Gargyantsa, A. Yu. Goritskyb, E. Yu. Panovcd

a Bauman Moscow State Technical University, Moscow, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
c Yaroslav-the-Wise Novgorod State University, Velikii Novgorod, Russia
d Peoples' Friendship University of Russia, Moscow, Russia
English version PDF (578 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.1070/SM9383
Abstract: A first-order quasilinear equation with an odd flux function that has a single point of inflexion at zero is studied. A method for constructing sign-alternating discontinuous entropy solutions of this equation, based on the Legendre transform, is proposed.
Bibliography: 18 titles.
Keywords: one-dimensional conservation laws, entropy solutions, Legendre transform.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation МК-1204.2020.1
5-100
Ministry of Science and Higher Education of the Russian Federation 0705-2020-0047
1.445.2016/1.4
Russian Foundation for Basic Research 17-01-00515-а
18-01-00472-а
The research by L. V. Gargyants was carried out within the Programme of the President of the Russian Federation for the state support of young Russian scientists (grant no. MK-1204.2020.1) and was also supported by the Ministry of Science and Higher Education of the Russian Federation (project no. 0705-2020-0047). The research by A. Yu. Goritsky was supported by the Russian Foundation for Basic Research (grant no. 17-01-00515-a). The research by E. Yu. Panov was carried out within the RUDN University Strategic Academic Leadership Program and the state assignment of the Ministry of Science and Higher Education of the Russian Federation (project no. 1.445.2016/1.4); it was also supported by the Russian Foundation for Basic Research (grant no. 18-01-00472-a).
Received: 20.02.2020
Bibliographic databases:
Document Type: Article
UDC: 517.95
MSC: Primary 35L65; Secondary 35L03
Language: English
Original paper language: Russian
Citation: L. V. Gargyants, A. Yu. Goritsky, E. Yu. Panov, “Constructing unbounded discontinuous solutions of scalar conservation laws using the Legendre transform”, Sb. Math., 212:4 (2021), 475–489
Citation in format AMSBIB
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\by L.~V.~Gargyants, A.~Yu.~Goritsky, E.~Yu.~Panov
\paper Constructing unbounded discontinuous solutions of scalar conservation laws using the Legendre transform
\jour Sb. Math.
\yr 2021
\vol 212
\issue 4
\pages 475--489
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\crossref{https://doi.org/10.1070/SM9383}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85109181207}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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