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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 1999, Volume 40, Issue 5, Pages 23–32 (Mi pmtf3135)  
This article is cited in 4 scientific papers (total in 4 papers)

Complete systems of conservation laws for two-layer shallow water models

V. V. Ostapenko

Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090
Full-text PDF (732 kB) Citations (4)
Abstract: A well-posedness criterion for a complete system of conservation laws is proposed that assumes maximum compatibility of the convexity domain of the closing conservation law with the domain of hyperbolicity of the model used. This criterion is used to obtain well-posed complete systems of conservation laws for the models of two-layer shallow water with a free-surface (model I) and with a rigid lid (model II).
Received: 23.09.1997
English version:
Journal of Applied Mechanics and Technical Physics, 1999, Volume 40, Issue 5, Pages 796–804
DOI: https://doi.org/10.1007/BF02468461
Bibliographic databases:
Document Type: Article
UDC: 532.59
Language: Russian
Citation: V. V. Ostapenko, “Complete systems of conservation laws for two-layer shallow water models”, Prikl. Mekh. Tekh. Fiz., 40:5 (1999), 23–32; J. Appl. Mech. Tech. Phys., 40:5 (1999), 796–804
Citation in format AMSBIB
\Bibitem{Ost99}
\by V.~V.~Ostapenko
\paper Complete systems of conservation laws for two-layer shallow water models
\jour Prikl. Mekh. Tekh. Fiz.
\yr 1999
\vol 40
\issue 5
\pages 23--32
\mathnet{http://mi.mathnet.ru/pmtf3135}
\elib{https://elibrary.ru/item.asp?id=35313665}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 1999
\vol 40
\issue 5
\pages 796--804
\crossref{https://doi.org/10.1007/BF02468461}
Linking options:
  • https://www.mathnet.ru/eng/pmtf3135
  • https://www.mathnet.ru/eng/pmtf/v40/i5/p23
    • This publication is cited in the following 4 articles:
    1. Janis Priede, “Self‐contained two‐layer shallow‐water theory of strong internal bores”, Stud Appl Math, 150:2 (2023), 457  crossref
    2. Eirik Holm Fyhn, Karl Yngve Lervåg, Åsmund Ervik, Øivind Wilhelmsen, “A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model”, Physics of Fluids, 31:12 (2019)  crossref
    3. T. G. Elizarova, A. V. Ivanov, “Regularized equations for numerical simulation of flows in the two-layer shallow water approximation”, Comput. Math. Math. Phys., 58:5 (2018), 714–734  mathnet  mathnet  crossref  crossref  isi  scopus
    4. P. E. Karabut, V. V. Ostapenko, “Problem of the decay of a small-amplitude discontinuity in two-layer shallow water: First approximation”, J. Appl. Mech. Tech. Phys., 52:5 (2011), 698–708  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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