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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 9, Pages 1586–1598 (Mi zvmmf10271)  

This article is cited in 2 scientific papers (total in 2 papers)

Systems of quasilinear conservation laws and algorithmization of variational principles

Yu. G. Rykov, O. B. Feodoritova

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

Abstract: A previously formulated new approach to the consideration of systems of quasilinear hyperbolic equations on the basis of variational principles is described in more detail in the case of special systems of three equations. It is shown that each field of characteristics can be represented as a solution of a variational problem. Moreover, the RankineЦHugoniot relations at the corner points of the characteristics or at the intersections of the characteristics of a single family hold automatically. In the simplest case of the Hopf equation, a numerical algorithm is constructed on the basis of a variational principle.

Key words: hyperbolic system, gas dynamics equations, characteristics, variational problem, discontinuous solutions, Rankine–Hugoniot relations, numerical algorithm.

DOI: https://doi.org/10.7868/S0044466915090148

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:9, 1554–1566

Bibliographic databases:

UDC: 519.634
Received: 24.02.2015

Citation: Yu. G. Rykov, O. B. Feodoritova, “Systems of quasilinear conservation laws and algorithmization of variational principles”, Zh. Vychisl. Mat. Mat. Fiz., 55:9 (2015), 1586–1598; Comput. Math. Math. Phys., 55:9 (2015), 1554–1566

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. G. Rykov, “Dvumernaya gazovaya dinamika bez davleniya i variatsionnyi printsip”, Preprinty IPM im. M. V. Keldysha, 2016, 094, 14 pp.  mathnet  crossref
    2. Yu. G. Rykov, “On the variational approach to systems of quasilinear conservation laws”, Proc. Steklov Inst. Math., 301 (2018), 213–227  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • ∆урнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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