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Mat. Sb., 2000, Volume 191, Number 1, Pages 127–157 (Mi msb450)  

This article is cited in 13 scientific papers (total in 13 papers)

On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws

E. Yu. Panov

Novgorod State University after Yaroslav the Wise

Abstract: Many-dimensional non-strictly hyperbolic systems of conservation laws with a radially degenerate flux function are considered. For such systems the set of entropies is defined and described, the concept of generalized entropy solution of the Cauchy problem is introduced, and the properties of generalized entropy solutions are studied. The class of strong generalized entropy solutions is distinguished, in which the Cauchy problem in question is uniquely soluble. A condition on the initial data is described that ensures that the generalized entropy solution is strong and therefore unique. Under this condition the convergence of the “vanishing viscosity” method is established. An example presented in the paper shows that a generalized entropy solution is not necessarily unique in the general case.

DOI: https://doi.org/10.4213/sm450

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English version:
Sbornik: Mathematics, 2000, 191:1, 121–150

Bibliographic databases:

UDC: 517.95
MSC: 35L65, 35L15
Received: 03.03.1999

Citation: E. Yu. Panov, “On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws”, Mat. Sb., 191:1 (2000), 127–157; Sb. Math., 191:1 (2000), 121–150

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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. Bressan A., “An ill posed Cauchy problem for a hyperbolic system in two space dimensions”, Rend. Sem. Mat. Univ. Padova, 110 (2003), 103–117  mathscinet  zmath  isi
    2. Panov E.Yu., “On infinite-dimensional Keyfitz-Kranzer systems of conservation laws”, Differ. Equ., 45:2 (2009), 274–278  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Ambrosio L., Crippa G., Figalli A., Spinolo L.V., “Some New Well-Posedness Results for Continuity and Transport Equations, and Applications to the Chromatography System”, SIAM Journal on Mathematical Analysis, 41:5 (2009), 1890–1920  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    4. Crippa G., Spinolo L.V., “An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws”, Communications on Pure and Applied Analysis, 9:5 (2010), 1283–1293  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Yun-guang Lu, “Existence of global bounded weak solutions to nonsymmetric systems of Keyfitz-Kranzer type”, Journal of Functional Analysis, 261:10 (2011), 2797–2815  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Lu Yu.-g., Gu F., “Existence of Global Bounded Weak Solutions to a Keyfitz-Kranzer System”, Commun. Math. Sci., 10:4 (2012), 1133–1142  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Ujjwal Koley, Nils Henrik Risebro, “Finite difference schemes for the symmetric Keyfitz–Kranzer system”, Z. Angew. Math. Phys, 2012  crossref  mathscinet  isi  scopus  scopus  scopus
    8. Yun-guang Lu, “Existence of global entropy solutions to general system of Keyfitz–Kranzer type”, Journal of Functional Analysis, 2013  crossref  mathscinet  isi  scopus  scopus  scopus
    9. N.H. Risebro, F. Weber, “A note on front tracking for the Keyfitz–Kranzer system”, Journal of Mathematical Analysis and Applications, 2013  crossref  mathscinet  isi  scopus  scopus  scopus
    10. Yun-Guang Lu, “Existence of Global Weak Entropy Solutions to Some Nonstrictly Hyperbolic Systems”, SIAM J. Math. Anal, 45:6 (2013), 3592  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    11. R.A.lexander De la Cruz Guerrero, J.C.arlos Juajibioy Otero, Leonardo Rendon, “Asymptotic Behavior of Global Entropy Solutions for Nonstrictly Hyperbolic Systems with Linear Damping”, International Journal of Differential Equations, 2014 (2014), 1  crossref  mathscinet  scopus  scopus  scopus
    12. Andreianov B. Donadello C. Ghoshal Sh.S. Razafison U., “on the Attainable Set For a Class of Triangular Systems of Conservation Laws”, J. Evol. Equ., 15:3 (2015), 503–532  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Yun-guang Lu, Xue-zhou Lu, C. Klingenberg, “The Cauchy problem for multiphase first-contact miscible models with viscous fingering”, Nonlinear Analysis: Real World Applications, 27 (2016), 43  crossref  mathscinet  zmath  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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