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Preprints of the Keldysh Institute of Applied Mathematics, 2014, 084, 22 pp. (Mi ipmp1936)  

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

On the methodology of variational representation of generalized solutions to quasi-linear hyperbolic two-equations systems

Yu. G. Rykov, O. B. Feodoritova
Full-text PDF (906 kB) Citations (2)
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Abstract: The paper contains further detailing of earlier formulated new approach to the study of quasi-linear hyperbolic systems on the basis of variational approach. The elaboration is got for the systems of two equations. It is shown that each characteristic field can be represented as the solution of certain variation calculus problem. At this the Hugoniot relations at the characteristics’ bents or when the characteristics of the same family intersect are fulfilled automatically. Also the paper describes the experience of numerical scheme construction on the basis of variational approach in the simplest case of Hopf equation. The work is written with “physical” level of rigor.
Keywords: hyperbolic system, characteristics, variational problem, discontinuous solutions, Hugoniot relations.
Document Type: Preprint
Language: Russian
Citation: Yu. G. Rykov, O. B. Feodoritova, “On the methodology of variational representation of generalized solutions to quasi-linear hyperbolic two-equations systems”, Keldysh Institute preprints, 2014, 084, 22 pp.
Citation in format AMSBIB
\Bibitem{RykFeo14}
\by Yu.~G.~Rykov, O.~B.~Feodoritova
\paper On the methodology of variational representation of generalized solutions to quasi-linear hyperbolic two-equations systems
\jour Keldysh Institute preprints
\yr 2014
\papernumber 084
\totalpages 22
\mathnet{http://mi.mathnet.ru/ipmp1936}
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  • https://www.mathnet.ru/eng/ipmp/y2014/p84
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Ïðåïðèíòû Èíñòèòóòà ïðèêëàäíîé ìàòåìàòèêè èì. Ì. Â. Êåëäûøà ÐÀÍ
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    Full-text PDF :37
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