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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 9, Pages 1586–1598
DOI: https://doi.org/10.7868/S0044466915090148 (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
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DOI: https://doi.org/10.7868/S0044466915090148
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 Rankine–Hugoniot 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.
Received: 24.02.2015
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 9, Pages 1554–1566
DOI: https://doi.org/10.1134/S0965542515090122
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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