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Mat. Zametki, 2011, Volume 89, Issue 2, Pages 300–315 (Mi mz6621)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Generalization of Conservation Law Theory to Certain Degenerate Parabolic Systems of Equations Describing Processes of Compressible Two-Phase Multicomponent Filtration

Yu. G. Rykov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: A degenerate parabolic system of equations of two-phase multicomponent filtration is considered. It is shown that this system can be treated as a system of conservation laws and the notions developed in the corresponding theory, such as hyperbolicity, shock waves, Hugoniot relations, stability conditions, Riemann problem, entropy, etc., can be applied to this system. The specific character of the use of such notions in the case of multicomponent filtration is demonstrated. An example of two-component mixture is used to describe the specific properties of solutions of the Riemann problem.

Keywords: degenerate parabolic system of equations, two-phase multicomponent filtration, conservation laws, Riemann problem, entropy, Darcy's law, Hugoniot relation

DOI: https://doi.org/10.4213/mzm6621

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English version:
Mathematical Notes, 2011, 89:2, 291–303

Bibliographic databases:

UDC: 517.956
Received: 17.12.2008
Revised: 16.04.2010

Citation: Yu. G. Rykov, “On the Generalization of Conservation Law Theory to Certain Degenerate Parabolic Systems of Equations Describing Processes of Compressible Two-Phase Multicomponent Filtration”, Mat. Zametki, 89:2 (2011), 300–315; Math. Notes, 89:2 (2011), 291–303

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Boehmer K., Schild K.-H., Schmitt B.A., “Dew Drops on Spider Webs: a Symmetry Breaking Bifurcation for a Parabolic Differential-Algebraic Equation”, J. Comput. Appl. Math., 254 (2013), 99–115  crossref  mathscinet  zmath  isi  scopus
    2. V. G. Lysov, Yu. G. Rykov, “O vychislenii fazovogo ravnovesiya v zadachakh mnogokomponentnoi filtratsii”, Preprinty IPM im. M. V. Keldysha, 2014, 094, 20 pp.  mathnet
    3. Rykov Yu.G., “on a Form of the System of Porous Media Flow Equations Convenient For the Construction of Parallel Algorithms”, Dokl. Math., 92:2 (2015), 606–608  crossref  mathscinet  zmath  isi  elib  scopus
    4. E. V. Borovik, A. V. Goncharov, Yu. G. Rykov, D. N. Tulyakov, “O raschete dvumernykh szhimaemykh filtratsionnykh techenii v sootvetstvii s metodologiei «szhimaemykh linii toka»”, Preprinty IPM im. M. V. Keldysha, 2016, 064, 12 pp.  mathnet  crossref
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